Hermitian-Einstein metrics for vector bundles on complete Kähler manifolds

Ni, Lei; Ren, Huaiyu

doi:10.1090/S0002-9947-00-02549-6

Hermitian-Einstein metrics for vector bundles on complete Kähler manifolds
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by Lei Ni and Huaiyu Ren PDF

Trans. Amer. Math. Soc. 353 (2001), 441-456 Request permission

Abstract:

In this paper, we prove the existence of Hermitian-Einstein metrics for holomorphic vector bundles on a class of complete Kähler manifolds which include Hermitian symmetric spaces of noncompact type without Euclidean factor, strictly pseudoconvex domains with Bergman metrics and the universal cover of Gromov hyperbolic manifolds etc. We also solve the Dirichlet problem at infinity for the Hermitian-Einstein equations on holomorphic vector bundles over strictly pseudoconvex domains.

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