Positively curved manifolds with large spherical rank (Q290752)
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scientific article; zbMATH DE number 6588944
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Positively curved manifolds with large spherical rank |
scientific article; zbMATH DE number 6588944 |
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Positively curved manifolds with large spherical rank (English)
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3 June 2016
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Summary: Rigidity results are obtained for Riemannian \(d\)-manifolds with \(\sec\geqslant1\) 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 \(d\neq6\), for Riemannian manifolds satisfying the Rakić duality principle, and for Kählerian manifolds.
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positive curvature
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higher rank
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spherical rank
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rigidity
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comparison theory
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