A note on Kahler manifolds with almost nonnegative bisectional curvature

2008/07/15 by Huang, Hong
#53C44 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0807.2310

Abstract

In this note we prove the following result: There is a positive constant ε(n,Λ) such that if Mⁿ is a simply connected compact Kahler 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 Mⁿ is diffeomorphic to the product M₁× ... × M_k, where each M_i is either a complex projective space or an irreducible Kahler-Hermitian symmetric space of rank ≥ 2. This resolves a conjecture of F. Fang under the additional upper bound restrictions on sectional curvature and diameter.

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