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December 2014 The Structure Theorem for the Cut Locus of a Certain Class of Cylinders of Revolution I
Pakkinee CHITSAKUL
Tokyo J. Math. 37(2): 473-484 (December 2014). DOI: 10.3836/tjm/1422452803

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. "The Structure Theorem for the Cut Locus of a Certain Class of Cylinders of Revolution I." Tokyo J. Math. 37 (2) 473 - 484, December 2014. https://doi.org/10.3836/tjm/1422452803

Information

Published: December 2014
First available in Project Euclid: 28 January 2015

zbMATH: 1317.53059
MathSciNet: MR3304691
Digital Object Identifier: 10.3836/tjm/1422452803

Subjects:
Primary: 53C22

Rights: Copyright © 2014 Publication Committee for the Tokyo Journal of Mathematics

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Vol.37 • No. 2 • December 2014
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