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Annals of Global Analysis and Geometry

, Volume 36, Issue 3, pp 323–325 | Cite as

A note on Kähler manifolds with almost nonnegative bisectional curvature

  • Hong HuangEmail author
Original Paper
  • 88 Downloads

Abstract

In this note, we prove the following result. There is a positive constant ε(n, Λ) such that if M n is a simply connected compact Kähler manifold with sectional curvature bounded from above by Λ, diameter bounded from above by 1, and with holomorphic bisectional curvature H ≥ −ε(n, Λ), then M n is diffeomorphic to the product M 1 × ⋯ × M k , where each M i is either a complex projective space or an irreducible Kähler–Hermitian symmetric space of rank ≥ 2. This resolves a conjecture of Fang under the additional upper bound restrictions on sectional curvature and diameter.

Mathematics Subject Classification (2000)

53C44 

Keywords

Kähler manifolds Almost nonnegative bisectional curvature Ricci flow 

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.School of Mathematical Sciences, Key Laboratory of Mathematics and Complex SystemsBeijing Normal UniversityBeijingPeoples’ Republic of China

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