2008/06/22 by Victor Bangert, Bangert, Victor, Eugene Gutkin +2
Computer Science · Mathematics · #37D40 #37E99 #53C22 #Computational Geometry and Mesh Generation #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #math.DG #math.DS #msc:37D40 #msc:37E99 #msc:53C22
paper · pdf · doi:10.48550/arxiv.0806.3572
15 pages, 4 figures
arxiv created 2008/06/22 · openalex publication_date 2008/06/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.