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Geometry of solutions of the geometric curve flows in space
  • Zehui Zhao,
  • Shiping Zhong,
  • Xinjie Wan
Zehui Zhao
School of Mathematics and Computer Sciences, Gannan Normal University
Shiping Zhong
School of Mathematics and Computer Sciences, Gannan Normal University, School of Mathematics and Computer Sciences, Gannan Normal University
Xinjie Wan
School of Mathematics and Computer Sciences, Gannan Normal University
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Abstract

In this study, we aim to investigate the geometry of surfaces corresponding to the geometry of solutions of the geometric curve flows in Euclidean 3-space 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 √ τ-normal trajectory surface in R 3 .