Secure two-dimensional tori are flat
Dynamical Systems
2008-06-24 v1 Differential Geometry
Abstract
A riemannian manifold is secure if the geodesics between any pair of points in the manifold can be blocked by a finite number of point obstacles. Compact, flat manifolds are secure. A standing conjecture says that these are the only secure, compact riemannian manifolds. The conjecture claims, in particular, that a riemannian torus of any dimension is secure if and only if it is flat. We prove this for two-dimensional tori.
Cite
@article{arxiv.0806.3572,
title = {Secure two-dimensional tori are flat},
author = {Victor Bangert and Eugene Gutkin},
journal= {arXiv preprint arXiv:0806.3572},
year = {2008}
}
Comments
15 pages, 4 figures