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Symmetry
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Symmetry and Its Application in Differential Geometry and Topology II
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Symmetry and Its Application in Differential Geometry and Topology II

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (31 December 2023) | Viewed by 16953

Special Issue Editors

Prof. Dr. Yanlin Li

E-Mail Website
Guest Editor
School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
Interests: singularity theory; differential geometry
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Tiehong Zhao

E-Mail Website
Guest Editor
School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
Interests: differential geometry
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Differential geometry is a branch of mathematics that has many applications not only in mathematics but in many other sciences, e.g., applications of the theory of curves and surfaces in the Euclidean plane and space. Geometry and Topology are quite related to Symmetry. Symmetric spaces commonly occur in differential geometry, representation theory and harmonic analysis. Differential geometry can be defined as the study of the geometry of differential manifolds, as well as of their submanifolds. In recent years, there has been a fast-growing interest in developing theories and tools for studying singular submanifolds. Because singular submanifolds are produced in physics, mechanics, and other application fields and are the breakthrough point to discover new problems. Therefore, it is of great scientific significance to study the geometric and topological properties of singular submanifolds. However, due to the existence of singular sets, the traditional analysis and geometric mathematical tools are no longer applicable, which makes the study of singular submanifolds difficult. In addition, applications of differential geometry and Topology can be found in almost any field of science, from biology to architecture. One of the most important applications of Topology is Topological Data Analysis (TDA). TDA combines ideas from Topology and also algebra, geometry, and analysis, with methods from statistics and computer science, for the purpose of analyzing contemporary data sets for which standard approaches are unsatisfactory. The motivating idea is that there is an underlying ''shape'' to the data and that new variants of some of the sophisticated tools of modern mathematics may be brought to bear to elucidate and learn from this structure. TDA has convincingly proved its utility in a wide range of applications in the life sciences, including in neuroscience, genomics, proteomics, evolution, and cancer biology, among other areas of research.

This Special Issue is intended to provide a series of papers focused on Symmetry and its applications of geometry and Topology, devoted to surveying the remarkable insights into many fields of sciences and exploring promising new developments.

Dr. Yanlin Li
Prof. Dr. Tiehong Zhao
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Symmetries in geometry
  • Symmetries in topology
  • Symmetries in singularity theory
  • Symmetries in topological data analysis
  • Symmetric and a-symmetric curve/surface pairs
  • Lorentz symmetry groups
  • Singularity theory
  • Morse theory/Discrete morse theory
  • Singularities
  • Singular submanifolds
  • Lightlike submanifolds
  • Biharmonic submanifolds
  • Warped product submanifolds
  • Differentiable manifolds
  • Submanifold theory
  • Legendrian duality
  • Front and frontal
  • Physics
  • Statistics
  • Topological data analysis
  • Computational topology
  • Applied topology and geometry
  • Topological and geometric methods in data analysis
  • Spectral and geometric methods in machine learning and data analysis
  • Persistent homology and cohomology, and applications
  • Neuroscience
  • Cancer biology
  • Genomics
  • Objects related to symmetry

Published Papers (20 papers)

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Research

18 pages, 306 KiB  
Article
Ricci Curvature Inequalities for Contact CR-Warped Product Submanifolds of an Odd Dimensional Sphere Admitting a Semi-Symmetric Metric Connection
by Meraj Ali Khan, Ibrahim Al-Dayel and Foued Aloui
Symmetry 2024, 16(1), 95; https://doi.org/10.3390/sym16010095 - 11 Jan 2024
Viewed by 729
Abstract
The primary objective of this paper is to explore contact CR-warped product submanifolds of Sasakian space forms equipped with a semi-symmetric metric connection. We thoroughly examine these submanifolds and establish various key findings. Furthermore, we derive an inequality relating the Ricci curvature to [...] Read more.
The primary objective of this paper is to explore contact CR-warped product submanifolds of Sasakian space forms equipped with a semi-symmetric metric connection. We thoroughly examine these submanifolds and establish various key findings. Furthermore, we derive an inequality relating the Ricci curvature to the mean curvature vector and warping function. Full article
(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology II)
20 pages, 338 KiB  
Article
Geometry of Warped Product Hemi-Slant Submanifolds of an S-Manifold
by Ahlam Al-Mutairi, Reem Al-Ghefari and Awatif Al-Jedani
Symmetry 2024, 16(1), 35; https://doi.org/10.3390/sym16010035 - 28 Dec 2023
Viewed by 750
Abstract
The purpose of this paper is to investigate a warped product of hemi-slant submanifolds on an S-manifold. We prove many interesting results for the existence of warped product hemi-slant submanifold of the type Mθ×fM⊥ with [...] Read more.
The purpose of this paper is to investigate a warped product of hemi-slant submanifolds on an S-manifold. We prove many interesting results for the existence of warped product hemi-slant submanifold of the type Mθ×fM⊥ with ξα∈Mθ of an S-manifold. For such submanifolds, a characterization theorem is proven. In addition, we form an inequality for the squared norm of the second fundamental form in terms of the warping function and the slant angle. We also provide some examples, and the equality case is also considered. Full article
(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology II)
19 pages, 1700 KiB  
Article
Investigation of Special Type-Π Smarandache Ruled Surfaces Due to Rotation Minimizing Darboux Frame in E3
by Emad Solouma, Ibrahim Al-Dayel, Meraj Ali Khan and Mohamed Abdelkawy
Symmetry 2023, 15(12), 2207; https://doi.org/10.3390/sym15122207 - 17 Dec 2023
Cited by 1 | Viewed by 861
Abstract
This study begins with the construction of type-Π Smarandache ruled surfaces, whose base curves are Smarandache curves derived by rotation-minimizing Darboux frame vectors of the curve in E3. The direction vectors of these surfaces are unit vectors that convert Smarandache [...] Read more.
This study begins with the construction of type-Π Smarandache ruled surfaces, whose base curves are Smarandache curves derived by rotation-minimizing Darboux frame vectors of the curve in E3. The direction vectors of these surfaces are unit vectors that convert Smarandache curves. The Gaussian and mean curvatures of the generated ruled surfaces are then separately calculated, and the surfaces are required to be minimal or developable. We report our main conclusions in terms of the angle between normal vectors and the relationship between normal curvature and geodesic curvature. For every surface, examples are provided, and the graphs of these surfaces are produced. Full article
(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology II)
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10 pages, 258 KiB  
Article
A Note on Shape Vector Fields on Hypersurfaces
by Suha B. Al-Shaikh
Symmetry 2023, 15(11), 2088; https://doi.org/10.3390/sym15112088 - 20 Nov 2023
Viewed by 652
Abstract
In this paper, we initiate the study of shape vector fields on the hypersurfaces of a Riemannian manifold. We use a shape vector field on a compact hypersurface of a Euclidean space to obtain a characterization of round spheres. We also find a [...] Read more.
In this paper, we initiate the study of shape vector fields on the hypersurfaces of a Riemannian manifold. We use a shape vector field on a compact hypersurface of a Euclidean space to obtain a characterization of round spheres. We also find a condition, under which a shape vector field that is on a compact hypersurface of a Euclidean space is a Killing vector field. Full article
(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology II)
11 pages, 390 KiB  
Article
A Surface Pencil with Bertrand Curves as Joint Curvature Lines in Euclidean Three-Space
by Sahar H. Nazra and Rashad A. Abdel-Baky
Symmetry 2023, 15(11), 1986; https://doi.org/10.3390/sym15111986 - 27 Oct 2023
Viewed by 668
Abstract
The main outcome of this work is the construction of a surface pencil with a similarity to Bertrand curves in Euclidean 3-space E3. Then, by exploiting the Serret–Frenet frame, we deduce the sufficient and necessary conditions for a surface pencil with [...] Read more.
The main outcome of this work is the construction of a surface pencil with a similarity to Bertrand curves in Euclidean 3-space E3. Then, by exploiting the Serret–Frenet frame, we deduce the sufficient and necessary conditions for a surface pencil with Bertrand curves as joint curvature lines. Consequently, the expansion to the ruled surface pencil is also designed. As demonstrations of our essential findings, we illustrate some models to emphasize the process. Full article
(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology II)
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16 pages, 371 KiB  
Article
Significance of Solitonic Fibers in Riemannian Submersions and Some Number Theoretic Applications
by Ali H. Hakami and Mohd Danish Siddiqi
Symmetry 2023, 15(10), 1841; https://doi.org/10.3390/sym15101841 - 28 Sep 2023
Cited by 1 | Viewed by 557
Abstract
In this manifestation, we explain the geometrisation of η-Ricci–Yamabe soliton and gradient η-Ricci–Yamabe soliton on Riemannian submersions with the canonical variation. Also, we prove any fiber of the same submersion with the canonical variation (in short CV) is an [...] Read more.
In this manifestation, we explain the geometrisation of η-Ricci–Yamabe soliton and gradient η-Ricci–Yamabe soliton on Riemannian submersions with the canonical variation. Also, we prove any fiber of the same submersion with the canonical variation (in short CV) is an η-Ricci–Yamabe soliton, which is called the solitonic fiber. Also, under the same setting, we inspect the η-Ricci–Yamabe soliton in Riemannian submersions with a φ(Q)-vector field. Moreover, we provide an example of Riemannian submersions, which illustrates our findings. Finally, we explore some applications of Riemannian submersion along with cohomology, Betti number, and Pontryagin classes in number theory. Full article
(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology II)
14 pages, 280 KiB  
Article
Projective Collineations in Warped Product Manifolds and (PRS)n Manifolds
by Sameh Shenawy, Uday Chand De, Nasser Bin Turki and Naeem Ahmad Pundeer
Symmetry 2023, 15(9), 1644; https://doi.org/10.3390/sym15091644 - 25 Aug 2023
Cited by 1 | Viewed by 639
Abstract
The current work first explores projective collineations on pseudo-Riemannian manifolds. Projective collineations, curvature collineations, and Ricci curvature collineations are examined in relation to one another. On warped product manifolds, the projective collineations of the form ζ=ζ1+ζ2 are [...] Read more.
The current work first explores projective collineations on pseudo-Riemannian manifolds. Projective collineations, curvature collineations, and Ricci curvature collineations are examined in relation to one another. On warped product manifolds, the projective collineations of the form ζ=ζ1+ζ2 are investigated. We scrutinize various inheritance aspects in projective collineations from warped product manifolds to its factor manifolds. This provides, for example, a partially negative solution to Besse’s problem regarding the existence of Einstein warped product manifolds. Finally, Pseudo-Ricci symmetric space-times admitting projective collineations are investigated. Full article
(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology II)
13 pages, 279 KiB  
Article
Impact of Semi-Symmetric Metric Connection on Homology of Warped Product Pointwise Semi-Slant Submanifolds of an Odd-Dimensional Sphere
by Ibrahim Al-Dayel and Meraj Ali Khan
Symmetry 2023, 15(8), 1606; https://doi.org/10.3390/sym15081606 - 19 Aug 2023
Viewed by 570
Abstract
Our paper explores warped product pointwise semi-slant submanifolds with a semi-symmetric metric connection in an odd-dimensional sphere and uncovers fundamental results. We also demonstrate how our findings can be applied to the homology of these submanifolds. Notably, we prove that under a specific [...] Read more.
Our paper explores warped product pointwise semi-slant submanifolds with a semi-symmetric metric connection in an odd-dimensional sphere and uncovers fundamental results. We also demonstrate how our findings can be applied to the homology of these submanifolds. Notably, we prove that under a specific condition, there are no stable currents for these submanifolds. This work adds valuable insights into the stability and behavior of warped product pointwise semi-slant submanifolds and sets the foundation for further research in this field. Full article
(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology II)
11 pages, 284 KiB  
Article
Some Curvature Properties of Finsler Warped Product Metrics
by Mengke Wu, Xiaoling Zhang, Lingen Sun and Lingyue Han
Symmetry 2023, 15(8), 1565; https://doi.org/10.3390/sym15081565 - 10 Aug 2023
Viewed by 565
Abstract
The class of warped product metrics can often be interpreted as key space models for the general theory of relativity and theory of space-time. In this paper, we first obtain the PDE characterization of Finsler warped product metrics with a vanishing Riemannian curvature. [...] Read more.
The class of warped product metrics can often be interpreted as key space models for the general theory of relativity and theory of space-time. In this paper, we first obtain the PDE characterization of Finsler warped product metrics with a vanishing Riemannian curvature. Moreover, we obtain equivalent conditions for locally Minkowski Finsler warped product spaces. Finally, we explicitly construct two types of non-Riemannian examples. Full article
(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology II)
13 pages, 291 KiB  
Article
Certain Results on the Lifts from an LP-Sasakian Manifold to Its Tangent Bundle Associated with a Quarter-Symmetric Metric Connection
by Mohammad Nazrul Islam Khan, Fatemah Mofarreh, Abdul Haseeb and Mohit Saxena
Symmetry 2023, 15(8), 1553; https://doi.org/10.3390/sym15081553 - 08 Aug 2023
Cited by 4 | Viewed by 1041
Abstract
The purpose of this study is to examine the complete lifts from the symmetric and concircular symmetric n-dimensional Lorentzian para-Sasakian manifolds (briefly, (LPS)n) to its tangent bundle TM associated with a Riemannian connection DC [...] Read more.
The purpose of this study is to examine the complete lifts from the symmetric and concircular symmetric n-dimensional Lorentzian para-Sasakian manifolds (briefly, (LPS)n) to its tangent bundle TM associated with a Riemannian connection DC and a quarter-symmetric metric connection (QSMC) D¯C. Full article
(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology II)
14 pages, 287 KiB  
Article
Concircular Vector Fields on Radical Anti-Invariant Lightlike Hypersurfaces of Almost Product-like Statistical Manifolds
by Esra Erkan
Symmetry 2023, 15(8), 1531; https://doi.org/10.3390/sym15081531 - 03 Aug 2023
Viewed by 504
Abstract
The motivation of the present study is to describe the main relations of the radical anti-invariant lightlike hypersurfaces of almost product-like statistical manifolds. We provide concircular vector fields on radical anti-invariant lightlike hypersurfaces and obtain some results involving these vector fields. Full article
(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology II)
21 pages, 370 KiB  
Article
Heyting Locally Small Spaces and Esakia Duality
by Artur Piękosz
Symmetry 2023, 15(7), 1342; https://doi.org/10.3390/sym15071342 - 30 Jun 2023
Viewed by 598
Abstract
We develop the theory of Heyting locally small spaces, including Stone-like dualities such as a new version of Esakia duality and a system of concrete isomorphisms and equivalences. In such a way, we continue building tame topology, realising Grothendieck’s ideas. We use up-spectral [...] Read more.
We develop the theory of Heyting locally small spaces, including Stone-like dualities such as a new version of Esakia duality and a system of concrete isomorphisms and equivalences. In such a way, we continue building tame topology, realising Grothendieck’s ideas. We use up-spectral spaces and define the standard up-spectralification of a Kolmogorov locally small space. This research gives more understanding of locally definable spaces over structures with topologies. Full article
(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology II)
12 pages, 314 KiB  
Article
Characterization of Ricci Almost Soliton on Lorentzian Manifolds
by Yanlin Li, Huchchappa A. Kumara, Mallannara Siddalingappa Siddesha and Devaraja Mallesha Naik
Symmetry 2023, 15(6), 1175; https://doi.org/10.3390/sym15061175 - 31 May 2023
Cited by 24 | Viewed by 1386
Abstract
Ricci solitons (RS) have an extensive background in modern physics and are extensively used in cosmology and general relativity. The focus of this work is to investigate Ricci almost solitons (RAS) on Lorentzian manifolds with a special metric connection [...] Read more.
Ricci solitons (RS) have an extensive background in modern physics and are extensively used in cosmology and general relativity. The focus of this work is to investigate Ricci almost solitons (RAS) on Lorentzian manifolds with a special metric connection called a semi-symmetric metric u-connection (SSM-connection). First, we show that any quasi-Einstein Lorentzian manifold having a SSM-connection, whose metric is RS, is Einstein manifold. A similar conclusion also holds for a Lorentzian manifold with SSM-connection admitting RS whose soliton vector Z is parallel to the vector u. Finally, we examine the gradient Ricci almost soliton (GRAS) on Lorentzian manifold admitting SSM-connection. Full article
(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology II)
17 pages, 322 KiB  
Article
Estimation of Ricci Curvature for Hemi-Slant Warped Product Submanifolds of Generalized Complex Space Forms and Their Applications
by Ibrahim Al-Dayel
Symmetry 2023, 15(6), 1156; https://doi.org/10.3390/sym15061156 - 26 May 2023
Viewed by 691
Abstract
In this paper, we estimate Ricci curvature inequalities for a hemi-slant warped product submanifold immersed isometrically in a generalized complex space form with a nearly Kaehler structure, and the equality cases are also discussed. Moreover, we also gave the equivalent version of these [...] Read more.
In this paper, we estimate Ricci curvature inequalities for a hemi-slant warped product submanifold immersed isometrically in a generalized complex space form with a nearly Kaehler structure, and the equality cases are also discussed. Moreover, we also gave the equivalent version of these inequalities. In a later study, we will exhibit the application of differential equations to the acquired results. In fact, we prove that the base manifold is isometric to Euclidean space under a specific condition. Full article
(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology II)
16 pages, 774 KiB  
Article
Spacelike Lines with Special Trajectories and Invariant Axodes
by Areej A. Almoneef and Rashad A. Abdel-Baky
Symmetry 2023, 15(5), 1087; https://doi.org/10.3390/sym15051087 - 15 May 2023
Viewed by 800
Abstract
The association between the instantaneous invariants of a one-parameter Lorentzian spatial movement and the spacelike lines with certain trajectories is considered in this study. To be more precise, we present a theoretical formulation of a Lorentzian inflection line congruence, which is the spatial [...] Read more.
The association between the instantaneous invariants of a one-parameter Lorentzian spatial movement and the spacelike lines with certain trajectories is considered in this study. To be more precise, we present a theoretical formulation of a Lorentzian inflection line congruence, which is the spatial symmetrical of the inflection circle of planar kinematics. Finally, we establish novel Lorentzian explanations for the Disteli and Euler–Savary formulae. Our results add to a better understanding of the interaction between axodes and Lorentzian spatial movements, with potential implications in fields such as robotics and mechanical engineering. Full article
(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology II)
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13 pages, 291 KiB  
Article
Two Special Types of Curves in Lorentzian α-Sasakian 3-Manifolds
by Xiawei Chen and Haiming Liu
Symmetry 2023, 15(5), 1077; https://doi.org/10.3390/sym15051077 - 12 May 2023
Viewed by 712
Abstract
In this paper, we focus on the research and analysis of the geometric properties and symmetry of slant curves and contact magnetic curves in Lorentzian α-Sasakian 3-manifolds. To do this, we define the notion of Lorentzian cross product. From the perspectives of [...] Read more.
In this paper, we focus on the research and analysis of the geometric properties and symmetry of slant curves and contact magnetic curves in Lorentzian α-Sasakian 3-manifolds. To do this, we define the notion of Lorentzian cross product. From the perspectives of the Legendre and non-geodesic curves, we found the ratio relationship between the curvature and torsion of the slant curve and contact magnetic curve in the Lorentzian α-Sasakian 3-manifolds. Moreover, we utilized the property of the contact magnetic curve to characterize the manifold as Lorentzian α-Sasakian and to find the slant curve type of the Frenet contact magnetic curve. Furthermore, we found an example to verify the geometric properties of the slant curve and contact magnetic curve in the Lorentzian α-Sasakian 3-manifolds. Full article
(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology II)
14 pages, 845 KiB  
Article
Sweeping Surfaces Due to Conjugate Bishop Frame in 3-Dimensional Lie Group
by Awatif Al-Jedani and Rashad Abdel-Baky
Symmetry 2023, 15(4), 910; https://doi.org/10.3390/sym15040910 - 14 Apr 2023
Cited by 1 | Viewed by 976
Abstract
In this work, we present a new Bishop frame for the conjugate curve of a curve in the 3-dimensional Lie group G3. With the help of this frame, we derive a parametric representation for a sweeping surface and show that the [...] Read more.
In this work, we present a new Bishop frame for the conjugate curve of a curve in the 3-dimensional Lie group G3. With the help of this frame, we derive a parametric representation for a sweeping surface and show that the parametric curves on this surface are curvature lines. We then examine the local singularities and convexity of this sweeping surface and establish the sufficient and necessary conditions for it to be a developable ruled surface. Additionally, we provide detailed explanations and examples of its applications. Full article
(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology II)
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16 pages, 1712 KiB  
Article
One-Parameter Hyperbolic Dual Spherical Movements and Timelike Ruled Surfaces
by Fatemah Mofarreh and Rashad A. Abdel-Baky
Symmetry 2023, 15(4), 902; https://doi.org/10.3390/sym15040902 - 13 Apr 2023
Viewed by 852
Abstract
In this paper, explicit expressions were improved for timelike ruled surfaces with the similarity of hyperbolic dual spherical movements. From this, the well known Hamilton and Mannhiem formulae of surfaces theory are attained at the hyperbolic line space. Then, by employing the E. [...] Read more.
In this paper, explicit expressions were improved for timelike ruled surfaces with the similarity of hyperbolic dual spherical movements. From this, the well known Hamilton and Mannhiem formulae of surfaces theory are attained at the hyperbolic line space. Then, by employing the E. Study map, a new timelike Plücker conoid is immediately founded and its geometrical properties are examined. In addition, via the height dual function, we specified the connection among the timelike ruled surface and the order of contact with its timelike Disteli-axis. Lastly, a classification for a timelike line to be a stationary timelike Disteli-axis is attained and explained in detail. Our findings contribute to a deeper realization of the cooperation between hyperbolic spatial movements and timelike ruled surfaces, with potential implementations in fields such as robotics and mechanical engineering. Full article
(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology II)
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11 pages, 277 KiB  
Article
Tangent Bundles of P-Sasakian Manifolds Endowed with a Quarter-Symmetric Metric Connection
by Mohammad Nazrul Islam Khan, Fatemah Mofarreh and Abdul Haseeb
Symmetry 2023, 15(3), 753; https://doi.org/10.3390/sym15030753 - 19 Mar 2023
Cited by 6 | Viewed by 1176
Abstract
The purpose of this study is to evaluate the curvature tensor and the Ricci tensor of a P-Sasakian manifold with respect to the quarter-symmetric metric connection on the tangent bundle TM. Certain results on a semisymmetric P-Sasakian manifold, generalized [...] Read more.
The purpose of this study is to evaluate the curvature tensor and the Ricci tensor of a P-Sasakian manifold with respect to the quarter-symmetric metric connection on the tangent bundle TM. Certain results on a semisymmetric P-Sasakian manifold, generalized recurrent P-Sasakian manifolds, and pseudo-symmetric P-Sasakian manifolds on TM are proved. Full article
(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology II)
19 pages, 328 KiB  
Article
Applying an Extended β-ϕ-Geraghty Contraction for Solving Coupled Ordinary Differential Equations
by Hasanen A. Hammad, Kamaleldin Abodayeh and Wasfi Shatanawi
Symmetry 2023, 15(3), 723; https://doi.org/10.3390/sym15030723 - 14 Mar 2023
Viewed by 1102
Abstract
In this paper, we introduce a new class of mappings called “generalized β-ϕ-Geraghty contraction-type mappings”. We use our new class to formulate and prove some coupled fixed points in the setting of partially ordered metric spaces. Our results generalize and [...] Read more.
In this paper, we introduce a new class of mappings called “generalized β-ϕ-Geraghty contraction-type mappings”. We use our new class to formulate and prove some coupled fixed points in the setting of partially ordered metric spaces. Our results generalize and unite several findings known in the literature. We also provide some examples to support and illustrate our theoretical results. Furthermore, we apply our results to discuss the existence and uniqueness of a solution to a coupled ordinary differential equation as an application of our finding. Full article
(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology II)
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