Existence and geometry of Hermitian metrics with constant second scalar curvature

Liangdi Zhang

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arXiv · 2601.20572

Existence and geometry of Hermitian metrics with constant second scalar curvature

Liangdi Zhang

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Abstract

We study Hermitian metrics with constant second scalar curvature on compact manifolds. We first consider a Yamabe-type problem for the second Bismut scalar curvature within balanced Hermitian conformal classes, and then analyze elliptic equations arising from constant second Chern scalar curvature within a fixed Hermitian conformal class and derive geometric consequences. Finally, under an Einstein-type condition on the second Chern curvature, a pluriclosed Gauduchon Hermitian metric has constant second Chern scalar curvature, which in certain cases further implies the existence of a K\"ahler-Einstein metric.

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Liangdi Zhang. 2026-01-28. Existence and geometry of Hermitian metrics with constant second scalar curvature. https://arxiv.org/abs/2601.20572

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