2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/156764A 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.Replaced a theorem from an earlier version with a reference and added a new theoremGeometric TopologyDifferential Geometrytext