2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/143217We prove the following rigidity theorem: For an n-dimensional compact Riemannian manifold with boundary whose Ricci curvature is bounded by n-1 from below, if its boundary is isometric to the standard sphere of dimension n-1 and totally geodesic, then the manifold is isometric to the standard hemisphere.The extrinsic boundary condition is relaxedDifferential Geometrytext