Existence of approximate Hermitian-Einstein structures on semistable principal bundles (Q713125)

The paper extends a result by A. Jacob saying that semistability of a vector bundle over a compact Kähler manifold is equivalent to existence of approximate Hermitian-Einstein structures, to the case of holomorphic principal \(G\)-bundles. Precisely, let \(G\) be a connected reductive linear algebraic group defined over \(\mathbb{C}.\) A holomorphic principal \(G\)-bundle is semistable if and only if it admits approximate Hermitian-Einstein structures. The proof goes via reduction to the case where \(G\) is semisimple.