A characterization of round spheres in terms of blocking light
Geometric Topology
2008-03-14 v2 Differential Geometry
Abstract
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.
Cite
@article{arxiv.0704.3642,
title = {A characterization of round spheres in terms of blocking light},
author = {Benjamin Schmidt and Juan Souto},
journal= {arXiv preprint arXiv:0704.3642},
year = {2008}
}
Comments
Replaced a theorem from an earlier version with a reference and added a new theorem