2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152255In this paper we give a generalisation of the Radius Rigidity theorem of F.Wilhelm. This is done by showing that if a Riemannian submersion of $S^{15}$ with 7-dimensional fibres has at least one fibre which is a great sphere then all the fibres are so. Some weaker than known conditions which force the existence of such a fibre are also discussed.8 pages LatexDifferential Geometrytext