Diameter rigidity for Kähler manifolds with positive bisectional curvature

Gang Liu; Yuan Yuan

doi:10.1007/s00209-018-2052-y

Diameter rigidity for Kähler manifolds with positive bisectional curvature

Gang Liu, Yuan Yuan

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

Let Mⁿ be a compact Kähler manifold with bisectional curvature bounded from below by 1. If diam(M)=π/2 and vol(M) > vol(CPⁿ) / 2 ⁿ, we prove that M is biholomorphically isometric to CPⁿ with the standard Fubini-Study metric.

Original language	English (US)
Pages (from-to)	1055-1061
Number of pages	7
Journal	Mathematische Zeitschrift
Volume	290
Issue number	3-4
DOIs	https://doi.org/10.1007/s00209-018-2052-y
State	Published - Dec 1 2018

ASJC Scopus subject areas

General Mathematics

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title = "Diameter rigidity for K{\"a}hler manifolds with positive bisectional curvature",

abstract = "Let Mn be a compact K{\"a}hler manifold with bisectional curvature bounded from below by 1. If diam(M)=π/2 and vol(M) > vol(CPn) / 2 n, we prove that M is biholomorphically isometric to CPn with the standard Fubini-Study metric.",

author = "Gang Liu and Yuan Yuan",

note = "Publisher Copyright: {\textcopyright} 2018, Springer-Verlag GmbH Germany, part of Springer Nature.",

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doi = "10.1007/s00209-018-2052-y",

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AU - Yuan, Yuan

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N2 - Let Mn be a compact Kähler manifold with bisectional curvature bounded from below by 1. If diam(M)=π/2 and vol(M) > vol(CPn) / 2 n, we prove that M is biholomorphically isometric to CPn with the standard Fubini-Study metric.

AB - Let Mn be a compact Kähler manifold with bisectional curvature bounded from below by 1. If diam(M)=π/2 and vol(M) > vol(CPn) / 2 n, we prove that M is biholomorphically isometric to CPn with the standard Fubini-Study metric.

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JO - Mathematische Zeitschrift

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Diameter rigidity for Kähler manifolds with positive bisectional curvature

Abstract

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