arXiv subjects
Publications and source records attributed to Pakkinee Chitsakul.
We study the behavior of geodesics on a Randers surface of revolution. The main tool is the extension of Clairaut relation from Riemannian case to the Randers case. Moreover, we show that our Randers surface of revolution can be embedded in a Minkowski space as hypersurface.
In the previous paper, 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.
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.