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

الأصل · EN

Let X be a compact Gauduchon manifold, and let E and V₀ be holomorphic vector bundles over X. Suppose that E is stable when considering all subsheaves preserved by a Higgs field θ∈ H⁰(End(E)⊗ V₀). Then a modified version of the Donaldson heat flow converges along a subsequence of times to a solution of a generalized Hermitian-Einstein equation, given by iΛF+[θ,θ†]=λI.