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Almost Diameter Rigidity for the Cayley Plane

Akhil Ranjan
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Abstract

In 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.

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BibTeXRIS

Akhil Ranjan. 1997-07-07. Almost Diameter Rigidity for the Cayley Plane. https://arxiv.org/abs/dg-ga/9707003

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