Affine Hermitian-Einstein Metrics

Details Affine Hermitian-Einstein Metrics Affine Hermitian-Einstein Metrics

2007-11-06

arxiv.org/abs/0711.0977v1

Mathematics

Differential Geometry

37 pages

Scientific paper

We develop a theory of stable bundles and affine Hermitian-Einstein metrics for flat vector bundles over a special affine manifold (a manifold admitting an atlas whose gluing maps are all locally constant volume-preserving affine maps). Our paper presents a parallel to Donaldson-Uhlenbeck-Yau's proof of the existence of Hermitian-Einstein metrics on K\"ahler manifolds, and the extension of this theorem by Li-Yau to the non-K\"ahler complex case of Gauduchon metrics. Our definition of stability involves only flat vector subbundles (and not singular subsheaves), and so is simpler than the complex case in some places.

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