Abstract
Let \(M^n\) be a compact Kähler manifold with bisectional curvature bounded from below by 1. If \(diam(M) = \pi / \sqrt{2}\) and \(vol(M)> vol({\mathbb {C}}{\mathbb {P}}^n)/ 2^n\), we prove that M is biholomorphically isometric to \({\mathbb {C}}{\mathbb {P}}^n\) with the standard Fubini-Study metric.
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Acknowledgements
We would like to thank Prof. Richard Bamler, L. F. Tam, Jiaping Wang, Steve Zelditch for their interest and helpful discussions.
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Gang Liu is supported by National Science Foundation Grant DMS-1406593. Yuan Yuan is supported by National Science Foundation Grant DMS-1412384 and Simons Foundation Grant (#429722 Yuan Yuan).
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Liu, G., Yuan, Y. Diameter rigidity for Kähler manifolds with positive bisectional curvature. Math. Z. 290, 1055–1061 (2018). https://doi.org/10.1007/s00209-018-2052-y
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DOI: https://doi.org/10.1007/s00209-018-2052-y