Geometry of solutions of the geometric curve flows in space

Zehui Zhao; Shiping Zhong; Xinjie Wan

doi:10.61383/ejam.20231340

Authors

Zehui Zhao School of Mathematics and Computer Sciences, Gannan Normal University, Ganzhou 431000, P.R. China
Shiping Zhong School of Mathematics and Computer Sciences, Gannan Normal University, Ganzhou 431000, P.R. China Corresponding Author
Xinjie Wan School of Mathematics and Computer Sciences, Gannan Normal University, Ganzhou 431000, P.R. China

DOI:

https://doi.org/10.61383/ejam.20231340

Keywords:

the Hasimoto surface, the shortening trajectory surface, the minimal trajectory surface, the $\sqrt{\tau}$-normal trajectory surface

Abstract

In this study, we aim at investigating the geometry of surfaces corresponding to the geometry of solutions of the geometric curve flows in Euclidean 3-space $\mathbb R^3$ considering the Frenet frame. In particular, we express some geometric properties and some characterizations of $u$-parameter curves and $t$-parameter curves of some trajectory surfaces including the Hasimoto surface, the shortening trajectory surface, the minimal trajectory surface, the $\sqrt{\tau}$-normal trajectory surface in $\mathbb R^3$.

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