Positively curved manifolds with large spherical rank

2014/09/26 by Schmidt, Benjamin, Shankar, Krishnan, Spatzier, Ralf
#53C20 #53C21 #53C30 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1409.7606

Abstract

Rigidity results are obtained for Riemannian d-manifolds with \sec \geqslant 1 and spherical rank at least d-2>0. 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 d-spheres when d ≠ 6, for Riemannian manifolds satisfying the Rakić duality principle, and for Kählerian manifolds.

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