# Representations of Rectifying Isotropic Curves and Their Centrodes in Complex 3-Space

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Preliminaries

**Definition**

**1.**

**Remark**

**1.**

**Proposition**

**1.**

**Definition**

**2.**

**Proposition**

**2.**

**Proposition**

**3.**

**Definition**

**3.**

**Remark**

**2.**

## 3. Rectifying Isotropic Curves

**Theorem**

**1.**

**Proof.**

**Theorem**

**2.**

- (1)
- $\langle r\left(s\right),r\left(s\right)\rangle =2a(s+b)$;
- (2)
- the tangent component $\langle r\left(s\right),{e}_{1}\left(s\right)\rangle =a$;
- (3)
- the binormal component $\langle r\left(s\right),{e}_{3}\left(s\right)\rangle =s+b$,

**Proof.**

**Theorem**

**3.**

**Proof.**

**Theorem**

**4.**

**Proof.**

**Corollary**

**1.**

**Theorem**

**5.**

**Corollary**

**2.**

## 4. The Centrodes of Rectifying Isotropic Curves

**Theorem**

**6.**

**Theorem**

**7.**

**Theorem**

**8.**

**Theorem**

**9.**

**Theorem**

**10.**

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Qian, J.; Yin, P.; Fu, X.; Wang, H.
Representations of Rectifying Isotropic Curves and Their Centrodes in Complex 3-Space. *Mathematics* **2021**, *9*, 1451.
https://doi.org/10.3390/math9121451

**AMA Style**

Qian J, Yin P, Fu X, Wang H.
Representations of Rectifying Isotropic Curves and Their Centrodes in Complex 3-Space. *Mathematics*. 2021; 9(12):1451.
https://doi.org/10.3390/math9121451

**Chicago/Turabian Style**

Qian, Jinhua, Pei Yin, Xueshan Fu, and Hongzeng Wang.
2021. "Representations of Rectifying Isotropic Curves and Their Centrodes in Complex 3-Space" *Mathematics* 9, no. 12: 1451.
https://doi.org/10.3390/math9121451