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arXiv · 2010.10925

Metric rigidity of Kahler manifolds with lower Ricci bounds and almost maximal volume

Ved Datar·Harish Seshadri·Jian Song
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Abstract

In this short note we prove that a Kahler manifold with lower Ricci curvature bound and almost maximal volume is Gromov-Hausdorff close to the projective space with the Fubini-Study metric. This is done by combining the recent results of Kewei Zhang and Yuchen Liu on holomorphic rigidity of such Kahler manifolds with the structure theorem of Tian-Wang for almost Einstein manifolds. This can be regarded as the complex analog of the result on Colding on the shape of Riemannian manifolds with almost maximal volume

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Ved Datar, Harish Seshadri, Jian Song. 2020-10-21. Metric rigidity of Kahler manifolds with lower Ricci bounds and almost maximal volume. https://arxiv.org/abs/2010.10925

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