A Kobayashi-Hitchin correspondence for I-+/--holomorphic bundles

摘要

In this paper, we introduce the notions of alpha-Hermitian-Einstein metric and alpha-stability for I-+/--holomorphic vector bundles on bi-Hermitian manifolds. Moreover, we establish a Kobayashi-Hitchin correspondence for I-+/--holomorphic vector bundles on bi-Hermitian manifolds. Examples of such vector bundles include generalized holomorphic bundles on generalized Kahler manifolds. We also show that alpha-stability of a vector bundle, in this sense, can depend on the parameter a. (C) 2015 Elsevier Inc. All rights reserved.