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

2013/11/29 by Pakkinee Chitsakul, Chitsakul, Pakkinee
Engineering · Mathematics · #53C22 #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Mathematics and Applications #Point processes and geometric inequalities #math.DG #msc:53C22

paper · pdf · doi:10.48550/arxiv.1311.7475

12 pages, no figures

arxiv created 2013/11/29 · openalex publication_date 2013/11/29 · arxiv updated 2013/12/02 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28

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.

Related

• The Structure Theorem for The cut locus of a Certain Class of Cylinders of Revolution II
• The cut locus of a Randers rotational 2-sphere of revolution
• A new family of latitudinally corrugated two-spheres of revolution with simple cut locus
• Generalized von Mangoldt surfaces of revolution and asymmetric two-spheres of revolution with simple cut locus structure
• The cut loci on ellipsoids and certain Liouville manifolds