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Substantial Riemannian submersions ofS 15 with 7-dimensional fibres

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Abstract

In this paper we show that a substantial Riemannian submersion ofS 15 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.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology, 400 076, Bombay, India

    Akhil Ranjan

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  1. Akhil Ranjan
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Correspondence to Akhil Ranjan.

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Ranjan, A. Substantial Riemannian submersions ofS 15 with 7-dimensional fibres. Proc. Indian Acad. Sci. (Math. Sci.) 107, 243–250 (1997). https://doi.org/10.1007/BF02867255

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  • DOI: https://doi.org/10.1007/BF02867255

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