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arXiv · 2106.09133

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

Xuemiao Chen·Richard A. Wentworth
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Abstract

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

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Xuemiao Chen, Richard A. Wentworth. 2021-06-16. The nonabelian Hodge correspondence for balanced hermitian metrics of Hodge-Riemann type. https://arxiv.org/abs/2106.09133

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