Geometry of solutions of the geometric curve flows in space

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
  • 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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Published

2023 Oct 29

How to Cite

[1]
Z. Zhao, S. Zhong, and X. Wan, “Geometry of solutions of the geometric curve flows in space”, Electron. J. Appl. Math., vol. 1, no. 3, pp. 16–25, Oct. 2023.

Issue

Section

Research Article
Received 2023 Jul 19
Accepted 2023 Oct 20
Published 2023 Oct 29