A Characterization of Curves that Lie on a Totally Umbilical Surface of a Space Form

Fuente: arXiv
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1. Verfasser: López, Rafael
Format: Preprint
Veröffentlicht: 2024
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author López, Rafael
author_facet López, Rafael
contents We give necessary and sufficient conditions on the curvature and the torsion of a regular curve of the space forms $\h^3$ and $\s^3$ to be contained in a totally umbilical surface. In case that the curve has constant torsion, we obtain the value of the curvature of the curve. Also numerical pictures of these curves are shown.
format Preprint
id arxiv_https___arxiv_org_abs_2411_19501
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A Characterization of Curves that Lie on a Totally Umbilical Surface of a Space Form
López, Rafael
Differential Geometry
53A04, 53A05, 53B20
We give necessary and sufficient conditions on the curvature and the torsion of a regular curve of the space forms $\h^3$ and $\s^3$ to be contained in a totally umbilical surface. In case that the curve has constant torsion, we obtain the value of the curvature of the curve. Also numerical pictures of these curves are shown.
title A Characterization of Curves that Lie on a Totally Umbilical Surface of a Space Form
topic Differential Geometry
53A04, 53A05, 53B20
url https://arxiv.org/abs/2411.19501