Positively curved manifolds with large spherical rank

Benjamin Schmidt; Krishnan Shankar; Ralf Spatzier

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arXiv · 1409.7606

Positively curved manifolds with large spherical rank

Benjamin Schmidt·Krishnan Shankar·Ralf Spatzier

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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 $d \neq 6$, for Riemannian manifolds satisfying the Raki\'c duality principle, and for K\"ahlerian manifolds.

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Benjamin Schmidt, Krishnan Shankar, Ralf Spatzier. 2014-09-26. Positively curved manifolds with large spherical rank. https://arxiv.org/abs/1409.7606

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