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- Title
A note on K ähler manifolds with almost nonnegative bisectional curvature.
- Authors
Hong Huang
- 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 K ähler 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 M1 × ⋯ × M k, where each M i is either a complex projective space or an irreducible K ähler–Hermitian symmetric space of rank ≥ 2. This resolves a conjecture of Fang under the additional upper bound restrictions on sectional curvature and diameter.
- Subjects
KAHLERIAN manifolds; HOLOMORPHIC functions; HERMITIAN symmetric spaces; SPACES of constant curvature; RICCI flow
- Publication
Annals of Global Analysis & Geometry, 2009, Vol 36, Issue 3, p323
- ISSN
0232-704X
- Publication type
Article
- DOI
10.1007/s10455-009-9165-9