Stable Higgs bundles and Hermitian-Einstein metrics on non-Kähler manifolds

Details Stable Higgs bundles and Hermitian-Einstein metrics on non-Kähler manifolds Stable Higgs bundles and Hermitian-Einstein metrics on non-Kähler manifolds

2011-10-17

arxiv.org/abs/1110.3768v1

Mathematics

Differential Geometry

21 pages

Scientific paper

If X is a compact Gauduchon manifold, we show that for a stable Higgs bundle
over X, the Donaldson heat flow converges along a subsequence of times to a
Hermitian-Einstein connection. This allows us to extend to the non-K\"ahler
case the correspondence between stable Higgs bundles and Hermitian-Einstein
connections first proven by Simpson on K\"aahler manifolds.

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