# Geometry of solutions of the geometric curve flows in space

## 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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*Electron. J. Appl. Math.*, vol. 1, no. 3, pp. 16–25, Oct. 2023.

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Copyright (c) 2023 Electronic Journal of Applied Mathematics

This work is licensed under a Creative Commons Attribution 4.0 International License.

Accepted 2023 Oct 20

Published 2023 Oct 29