Substantial Riemannian Submersions of S(15) with 7- dimensional fibres

Details Substantial Riemannian Submersions of S(15) with 7- dimensional fibres Substantial Riemannian Submersions of S(15) with 7- dimensional fibres

1995-10-31

arxiv.org/abs/dg-ga/9510009v1

Mathematics

Differential Geometry

10 pages, Latex (email: aranjan@ganit.math.iitb.ernet.in)

Scientific paper

In 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.

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