• Substantial Riemannian submersions ofS15 with 7-dimensional fibres

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      https://www.ias.ac.in/article/fulltext/pmsc/107/03/0243-0250

    • Keywords

       

      Riemannian submersions; Euler class; connections; holonomy groups; second fundamental form

    • Abstract

       

      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.

    • Author Affiliations

       

      Akhil Ranjan1

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

       
  • Proceedings – Mathematical Sciences | News

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