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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1023350-0
PII: S 0002-9939(1990)1023350-0
Keywords: Holomorphic vector bundle, Ricci curvature, Chern numbers
Article copyright: © Copyright 1990 American Mathematical Society