2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/33397We deal with seven dimensional compact Riemannian manifolds of positive curvature which admit a cohomogeneity one action by a compact Lie group G. We prove that the manifold is diffeomorphic to a sphere if the dimension of the semisimple part of G is bigger than 6.7 pages; this new version contains one more important exampleDifferential Geometry53C21 57S15 (primary)text