Long geodesics on convex surfaces
Differential Geometry
2018-10-01 v2 History and Overview
Abstract
We review the theory of intrinsic geometry of convex surfaces in the Euclidean space and prove the following theorem: if the surface of a convex body K contains arbitrary long closed simple geodesics, then K is an isosceles tetrahedron.
Keywords
Cite
@article{arxiv.1702.05172,
title = {Long geodesics on convex surfaces},
author = {Arseniy Akopyan and Anton Petrunin},
journal= {arXiv preprint arXiv:1702.05172},
year = {2018}
}
Comments
8 pages, 10 figures