Datar, V and Seshadri, H and Song, J
(2021)
*Metric rigidity of kÃ¤hler manifolds with lower ricci bounds and almost maximal volume.*
In: Proceedings of the American Mathematical Society, 149
(8).
pp. 3569-3574.

## Abstract

In this short note we prove that a KÃ¤hler 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 on holomorphic rigidity of such KÃ¤hler manifolds (see Gang Liu Asian J. Math. 18 (2014), 69â��99) with the structure theorem of Tian-Wang (see Gang Tian and Bing Wang J. Amer. Math. Soc 28 (2015), 1169â��1209) 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. Â© 2021 American Mathematical Society

Item Type: | Journal Article |
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Publication: | Proceedings of the American Mathematical Society |

Publisher: | American Mathematical Society |

Additional Information: | The copyright for this article belongs to American Mathematical Society |

Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |

Date Deposited: | 27 Aug 2021 06:04 |

Last Modified: | 27 Aug 2021 06:04 |

URI: | http://eprints.iisc.ac.in/id/eprint/69352 |

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