Positively curved manifolds with large spherical rank
Benjamin Schmidt
Michigan State University, East Lansing, USAKrishnan Shankar
University of Oklahoma, Norman, USARalf Spatzier
University of Michigan, Ann Arbor, USA
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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