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arXiv · 1311.7475

The Structure Theorem for The Cut Locus of a Certain Class of Cylinders of Revolution I

Pakkinee Chitsakul
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Abstract

The aim of this paper is to determine the structure of the cut locus for a class of surfaces of revolution homeomorphic to a cylinder. Let $M$ denote a cylinder of revolution which admits a reflective symmetry fixing a parallel called the equator of $M.$ It will be proved that the cut locus of a point $p$ of $M$ is a subset of the union of the meridian and the parallel opposite to $p$ respectively, if the Gaussian curvature of $M$ is decreasing on each upper half meridian.

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Pakkinee Chitsakul. 2013-11-29. The Structure Theorem for The Cut Locus of a Certain Class of Cylinders of Revolution I. https://arxiv.org/abs/1311.7475

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