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.
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页码：801 / 808
页数：8
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