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arXiv · 2609.14363

On Compact Hermitian Surfaces With Positive Strominger-Bismut Sectional Curvature

Qingsong Wang·Shing-Tung Yau·Fangyang Zheng
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Abstract

In an earlier work, Yau and Zheng proposed a Hermitian analogue of a weak form of the Frankel conjecture, which states that any compact Hermitian manifold with positive Strominger-Bismut sectional curvature must be biholomorphic to the complex projective space. In this article, we confirm the conjecture in complex dimension two. This is achieved by a vanishing theorem for anti-self-dual harmonic 2-forms on such surfaces, utilizing a curvature decomposition formula by Ferreira and a refined Kato inequality.

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Qingsong Wang, Shing-Tung Yau, Fangyang Zheng. 2026-09-13. On Compact Hermitian Surfaces With Positive Strominger-Bismut Sectional Curvature. https://arxiv.org/abs/2609.14363

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