A NOTE FOR A GENERALIZATION OF THE DIFFERENTIAL EQUATION OF SPHERICAL CURVES

被引：0

作者：

Niang, Athoumane ^{[1
]}

Ndiaye, Ameth ^{[2
]}

机构：

[1] UCAD, Dept Math & Informat, Fac Sci & Tech, BP 5005, Dakar, Senegal

[2] UCAD, Dept Math, Fac Sci & Technol Educ & Format, Dakar 5036, Senegal

来源：

FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS | 2021年 / 36卷 / 04期

关键词：

spherical curves; differential geometry; Frenet equations; EXPLICIT CHARACTERIZATION;

D O I：

10.22190/FUMI200830059N

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The differential equation characterizing a spherical curve in R-3 expresses the radius of curvature of the curve in terms of its torsion. In this paper, we have given a generalization of this equation for a curve lying in an arbitrary surface in R-3. Moreover, we have established the analogue of the Frenet equations for a curve lying in a surface of R-3. We have also revisited some formulas for the geodesic torsion of a curve lying in a surface of R-3.

引用

页码：801 / 808

页数：8

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