2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/209720We calculate the cohomology rings of a collection of seven dimensional manifolds supporting an S^3 x S^3-action with one dimensional orbit space. These manifolds are of interest to differential geometers studying non-negative and positive sectional curvature. From this collection, we identify several families of manifolds for which there exist well-known topological invariants distinguishing homeomorphism and diffeomorphism types.25 pages; co-author addedDifferential GeometryAlgebraic Topology57R19 (Primary) 53C25 (Secondary)text