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

Athoumane Niang, Ameth Ndiaye

DOI Number
https://doi.org/10.22190/FUMI200830059N
First page
801
Last page
808

Abstract


The differential equation characterizing a spherical curve in $\mathbb{R}^3$ expresses the radius of curvature of the curve in terms of its torsion. In this paper we give a generalization of this equation for a curve lying in an arbitrary surface in $\mathbb{R}^3$. Moreover we establish the analogue of the Frenet equations for a curve lying in a surface of $\mathbb{R}^3$. We have also revisited some formulas for the geodesic torsion of a curve lying in a surface of $\mathbb{R}^3$.

Keywords

spherical curves, differential geometry, Frenet equations

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References


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DOI: https://doi.org/10.22190/FUMI200830059N

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