2012/11/30 by Eugene Gutkin, Eugène Gutkin, Gutkin, Eugene
Mathematics · #Advanced Algebra and Geometry #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG #math.DS
paper · pdf · doi:10.48550/arxiv.1211.7291
Minor editorial changes
openalex publication_date 2012/11/30 · arxiv created 2013/01/11 · arxiv updated 2013/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a connected Lie group acting locally simply transitively on a manifold M. By connecting curves in M we mean the orbits of one-parameter subgroups of G. To block a pair of points m1,m2∈ M is to find a finite set B⊂ M∖m1,m2 such that every connecting curve joining m1 and m2 intersects B. The homogeneous space M is blockable if every pair of points in M can be blocked. Motivated by the geodesic security [4], we conjecture that the only blockable homogeneous spaces of finite volume are the tori. Here we establish the conjecture for nilmanifolds.