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On almost Einstein holomorphic vector bundles over Hermitian surfaces

Author: Novica Blažić
Journal: Proc. Amer. Math. Soc. 110 (1990), 201-209
MSC: Primary 53C25; Secondary 32L05, 53C55, 57R20
MathSciNet review: 1023350
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Abstract: We study holomorphic vector bundles $ \left( {E,h} \right)$ of rank 2 over a compact Hermitian surface $ \left( {M,g} \right)$. Then the notion of a metric with a $ k$-pinched Ricci curvature is introduced and it represents the generalization of the Einstein condition. Some necessary topological conditions for existence of a metric $ h$ with $ k$-pinched $ \left( {0 \leq k \leq 1} \right)$ Ricci curvature are obtained.

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Keywords: Holomorphic vector bundle, Ricci curvature, Chern numbers
Article copyright: © Copyright 1990 American Mathematical Society