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Author: search.filters.author.Chitsakul, PakkineeSubject: search.filters.subject.Cut locus

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    The Structure Theorem for the Cut Locus of a Certain Class of Cylinders of Revolution II
    (2015-06-01)
    Chitsakul, Pakkinee
    ;
    Furuya, Y.
    In the previous paper [C], the structure of the cut locus was determined for a class of surfaces of revolution homeomorphic to a cylinder. In this paper, we prove the structure theorem of the cut locus for a wider class of surfaces of revolution homeomorphic to a cylinder.
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    The structure theorem for the cut locus of a certain class of cylinders of revolution I
    (2014-12-01)
    Chitsakul, Pakkinee
    ;
    Komori-Furuya, Y.
    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.