Positively curved manifolds with large spherical rank

  • Benjamin Schmidt

    Michigan State University, East Lansing, USA
  • Krishnan Shankar

    University of Oklahoma, Norman, USA
  • Ralf Spatzier

    University of Michigan, Ann Arbor, USA

Abstract

Rigidity results are obtained for Riemannian -manifolds with and spherical rank at least . Conjecturally, all such manifolds are locally isometric to a round sphere or complex projective space with the (symmetric) Fubini–Study metric. This conjecture is verified in all odd dimensions, for metrics on -spheres when , for Riemannian manifolds satisfying the Rakić duality principle, and for Kählerian manifolds.

Cite this article

Benjamin Schmidt, Krishnan Shankar, Ralf Spatzier, Positively curved manifolds with large spherical rank. Comment. Math. Helv. 91 (2016), no. 2, pp. 219–251

DOI 10.4171/CMH/384