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arXiv · 2411.19501

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

Rafael López
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Abstract

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.

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Rafael López. 2024-11-29. A Characterization of Curves that Lie on a Totally Umbilical Surface of a Space Form. https://arxiv.org/abs/2411.19501

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