A Characterization of Curves that Lie on a Totally Umbilical Surface of a Space Form
Abstract
We give necessary and sufficient conditions on the curvature and the torsion of a regular curve of the space forms 3 and 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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