Existence of approximate Hermitian-Einstein structures on semistable principal bundles

Mathematics – Differential Geometry

Scientific paper

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7 pages, Bulletin des Sciences Math\'ematiques (to appear)

Scientific paper

10.1016/j.bulsci.2012.02.005

Let E_G be a principal G-bundle over a compact connected K\"ahler manifold,
where G is a connected reductive complex linear algebraic group. We show that
E_G is semistable if and only if it admits approximate Hermitian-Einstein
structures.

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