Substantial Riemannian submersions ofS15 with 7-dimensional fibres
In this paper we show that a substantial Riemannian submersion ofS15 with 7-dimensional fibres is congruent to the standard Hopf fibration. As a consequence we prove a slightly weak form of the diameter rigidity theorem for the Cayley plane which is considerably stronger than the very recent radius rigidity theorem of Wilhelm.
Volume 131, 2021
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