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This paper extends the nonabelian Hodge correspondence for Kaehler manifoldsto a larger class of hermitian metrics on complex manifolds called balanced ofHodge-Riemann type. Essentially, it grows out of a few key observations so thatthe known results, especially the Donaldson-Uhlenbeck-Yau theorem andCorlette's theorem, can be applied in our setting. Though not necessarilyKaehler, we show that the Sampson-Siu Theorem proving that harmonic maps arepluriharmonic remains valid for a slightly smaller class by using the knownargument. Special important examples include those balanced metrics arisingfrom multipolarizations.

The nonabelian Hodge correspondence for balanced hermitian metrics of Hodge-Riemann type