Manifolds with nonnegative curvature operator of the second kind

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Issue Date
2023-01-13
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Authors
Li, Xiaolong
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Citation

Li, X. (2023). Manifolds with nonnegative curvature operator of the second kind. Communications in Contemporary Mathematics, 2350003. https://doi.org/10.1142/S0219199723500037

Abstract

We investigate the curvature operator of the second kind on Riemannian manifolds and prove several classification results. The first one asserts that a closed Riemannian manifold with three-positive curvature operator of the second kind is diffeomorphic to a spherical space form, improving a recent result of Cao?Gursky?Tran assuming two-positivity. The second one states that a closed Riemannian manifold with three-nonnegative curvature operator of the second kind is either diffeomorphic to a spherical space form, or flat, or isometric to a quotient of a compact irreducible symmetric space. This settles the nonnegativity part of Nishikawa?s conjecture under a weaker assumption.

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