2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/113020Let Pi: M -> B be an onto maximal rank map or a Riemannian submersion between Riemannian manifolds M and B. Initially, we prove necessary and sufficient conditions for any fiber F to be roughly isometric to M. Then, we prove necessary and sufficient conditions for Pi to be a rough isometry. As a corollary M is roughly isometric to FxB.25 pages, 7 figuresDifferential Geometry53C20text