A characterization of round spheres in terms of blocking light

  • Benjamin Schmidt

    Michigan State University, East Lansing, USA
  • Juan Souto

    Université de Rennes 1, France

Abstract

A closed Riemannian manifold is said to have cross (compact rank one symmetric space) blocking if whenever are less than the diameter apart, all light rays from can be shaded away from with at most two point shades. Similarly, a closed Riemannian manifold is said to have sphere blocking if for each all the light rays from are shaded away from by a single point shade. We prove that Riemannian manifolds with cross and sphere blocking are isometric to round spheres.

Cite this article

Benjamin Schmidt, Juan Souto, A characterization of round spheres in terms of blocking light. Comment. Math. Helv. 85 (2010), no. 2, pp. 259–271

DOI 10.4171/CMH/195