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arXiv · 2510.06648

K\"ahlerness of compact Hermitian surfaces under semi-definite Strominger-Bismut-Ricci curvatures

Liangdi Zhang
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Abstract

We prove several K\"ahlerness criteria for compact Hermitian surfaces under semi-definiteness assumptions on natural Ricci curvatures of the Strominger-Bismut connection. The key tools for proving these results are explicit identities relating these Ricci curvatures to the torsion of the Strominger-Bismut connection, together with corresponding Chern number identities on compact Hermitian surfaces. The results may be viewed as Strominger-Bismut analogues and reformulations of Yang's K\"ahlerness criteria for compact complex surfaces.

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Liangdi Zhang. 2025-10-08. K\"ahlerness of compact Hermitian surfaces under semi-definite Strominger-Bismut-Ricci curvatures. https://arxiv.org/abs/2510.06648

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