On Strominger space forms

Shuwen Chen; Fangyang Zheng

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arXiv · 2111.07108

On Strominger space forms

Shuwen Chen·Fangyang Zheng

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Abstract

In this article, we propose the following conjecture: if the Strominger connection of a compact Hermitian manifold has constant non-zero holomorphic sectional curvature, then the Hermitian metric must be K\"ahler. The main result of this article is to confirm the conjecture in dimension $2$. We also verify the conjecture in higher dimensions in a couple of special situations.

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Shuwen Chen, Fangyang Zheng. 2021-11-13. On Strominger space forms. https://arxiv.org/abs/2111.07108

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