Diameter rigidity for Kähler manifolds with positive bisectional curvature

Gang Liu, Yuan Yuan

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.

Journal: Mathematische Zeitschrift (2018)

DOI: https://doi.org/10.1007/s00209-018-2052-y