The non-abelian Hodge correspondence on some non-Kähler manifolds

On the existence of harmonic metrics on non‐Hermitian Yang–Mills bundles

“…Donaldson [9] and Corlette [6] proved that $$(E,D)$$ admits a harmonic metric if and only if it is semisimple. This result has also been extended to some noncompact or non‐Kähler manifolds by Jost–Zuo [17, 18], Simpson [25], Mochizuki [21], Collins–Jacob–Yau [5], Pan–Zhang–Zhang [23] and Wu–Zhang [28].…”