English

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

R2 v1 2026-06-22T18:20:46.013Z