Almost Diameter Rigidity for the Cayley Plane

Details Almost Diameter Rigidity for the Cayley Plane Almost Diameter Rigidity for the Cayley Plane

1997-07-07

arxiv.org/abs/dg-ga/9707003v1

Mathematics

Differential Geometry

8 pages Latex

Scientific paper

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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