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On Compact Hermitian Surfaces With Positive Strominger-Bismut Sectional Curvature
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.
Related
- Positivity of the canonical bundle and Hermitian metrics with quasi-negative holomorphic sectional curvature
- Hermitian manifolds with constant holomorphic sectional curvature or real bisectional curvature
- Hermitian connections with parallel torsion and constant holomorphic sectional curvature
- Hermitian threefolds with constant holomorphic sectional curvature
- Positive scalar curvature Kähler cones on compact complex surfaces
BibTeX
@misc{wang2026compact,
title = {{On Compact Hermitian Surfaces With Positive Strominger-Bismut Sectional Curvature}},
author = {Qingsong Wang and Shing-Tung Yau and Fangyang Zheng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14363},
eprint = {2609.14363},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14363},
}
RIS
TY - UNPB
TI - On Compact Hermitian Surfaces With Positive Strominger-Bismut Sectional Curvature
AU - Qingsong Wang
AU - Shing-Tung Yau
AU - Fangyang Zheng
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.14363
UR - https://arxiv.org/abs/2609.14363
AB - 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.
ER -