Long geodesics on convex surfaces
arXiv:1702.05172 · doi:10.1007/s00283-018-9795-5
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.
8 pages, 10 figures