Mathematics

CLC number: O175

Shapes of Regular Curves Defined by Hyperbolic Functions

由双曲函数定义的正则曲线的形状

¹ School of Science, Huzhou University, Huzhou 313000, Zhejiang, China
² Shanghai Aerospace Equipments Manufacturing Co., Ltd., Shanghai 200240, China

Received: 4 May 2024

Abstract

This article discusses the shapes of a class of regular curves defined by hyperbolic functions. We first make a preliminary judgment using its torsion and then get more precise descriptions using its curvature and algebraic invariants. In addition, we study the shape of the generalization of the curve.

摘要

本文讨论了一类由双曲函数定义的正则曲线的形状。我们首先利用曲线的挠率对曲线进行初步判断，然后利用曲率和代数不变量对曲线进行更精确的描述。此外，我们还对这类曲线更一般的情况进行了研究。