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arXiv · 1411.3416

A Kobayashi-Hitchin correspondence for $I_\pm$-holomorphic bundles

Shengda Hu·Ruxandra Moraru·Reza Seyyedali
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Abstract

In this paper, we introduce the notions of $\alpha$-Hermitian-Einstein metric and $\alpha$-stability for $I_\pm$-holomorphic vector bundles on bi-Hermitian manifolds. Moreover, we establish a Kobayashi-Hitchin correspondence for $I_\pm$-holomorphic vector bundles on bi-Hermitian manifolds. Examples of such vector bundles include generalized holomorphic bundles on generalized K\"ahler manifolds. We also show that $\alpha$-stability of a vector bundle, in this sense, can depend on the parameter $\alpha$.

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BibTeXRIS

Shengda Hu, Ruxandra Moraru, Reza Seyyedali. 2014-11-13. A Kobayashi-Hitchin correspondence for $I_\pm$-holomorphic bundles. https://arxiv.org/abs/1411.3416

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