Pseudo-Riemannian Metrics and Applications
A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Geometry and Topology".
Deadline for manuscript submissions: closed (30 April 2020) | Viewed by 8097
Special Issue Editor
Special Issue Information
Dear Colleagues,
Pseudo-Riemannian metrics are ubiquitous in differential geometry and its applications to theoretical physics. The study of the geometry of an n-dimensional manifold, once an inner product is assigned to the tangent space of each point, started with the revolutionary work of Riemann in the middle of the 19th century. In the first decades of the 20th century, the mathematical formulation of Einstein’s theory of relativity gave an exceptional impulse to the study of nondegenerate metrics. Since then, the relevance and applications of pseudo-Riemannian metrics has grown steadily. Among the recent achievements in this area, we can mention Perelman’s proof of the Poincaré Conjecture as an example.
The purpose of this Special Issue is to collect original and survey papers concerning relevant state-of-the-art results on pseudo-Riemannian metrics and their applications to Physics. A non-exhaustive list of topics includes homogeneous pseudo-Riemannian manifolds, Lorentzian manifolds, special curvature properties, tangent and unit tangent sphere bundles, Einstein manifolds and Ricci solitons, geodesic and magnetic curves, geometry of submanifolds, pseudo-Riemannian Lie groups, symmetries, special connections and metrics, methods of (pseudo-)Riemannian geometry, and harmonic maps.
Prof. Dr. Giovanni Calvaruso
Guest Editor
Manuscript Submission Information
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Keywords
- Differential geometry
- Pseudo-Riemannian metrics
- Lorentzian metrics
- Homogeneous manifolds
- Lie groups
- Symmetries
- Geodesics
- Magnetic curves
- Curvature
- Geometry of submanifolds
- Special connections and metrics
- Einstein manifolds
- Ricci solitons
- Harmonic maps
- Applications to physics
