Umbilical routes along geodesics and hypercycles in the hyperbolic space

Maciej Czarnecki

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arXiv · 1712.01950

Umbilical routes along geodesics and hypercycles in the hyperbolic space

Maciej Czarnecki

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Abstract

Given a geodesic line $\gamma$ the hyperbolic space $\mathbb H^n$ we formulate a necessary and sufficient condition for a function along this geodesic which measure the mean curvature of totally umbilical leaves of a foliation orthogonal to $\gamma$. Then we extend the result to $\gamma$ being a hypercycle i.e. a geodesic on a hypersurface equidistant from the totally geodesic one.

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BibTeX RIS

Maciej Czarnecki. 2017-12-05. Umbilical routes along geodesics and hypercycles in the hyperbolic space. https://arxiv.org/abs/1712.01950

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