A characterization of round spheres in terms of blocking light

Details A characterization of round spheres in terms of blocking light A characterization of round spheres in terms of blocking light

2007-04-27

arxiv.org/abs/0704.3642v2

Mathematics

Geometric Topology

Replaced a theorem from an earlier version with a reference and added a new theorem

Scientific paper

A closed Riemannian manifold is said to have cross blocking if whenever distinct points p and q are at distance less than the diameter, all light rays from p can be shaded away from q with at most two point shades. Similarly, a closed Riemannian manifold is said to have sphere blocking if for each point p, all the light rays from p are shaded away from p by a single point shade. We prove that Riemannian manifolds with cross and sphere blocking are isometric to round spheres.

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