2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152080In this paper we show that a substantial Riemannian submersion of S(15) with 7- dimensional fibres is congruent to the standard Hopf fibration. As a consequence we prove a slightly weak form of of the Diameter Rigidity theorem for the Cayley plane which is considerably stronger than the very recent Radius Rigidity Theorem of Wilhelm.10 pages, Latex (email: aranjan@ganit.math.iitb.ernet.in)Differential Geometrytext