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On Strominger Space Forms

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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 Kähler. 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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Acknowledgements

The second-named author would like to thank Haojie Chen, Xiaolan Nie, Kai Tang, Bo Yang, and Quanting Zhao for helpful discussions. Zheng is partially supported by National Natural Science Foundations of China with the Grant Nos. 12071050 and 12141101, Chongqing Grant cstc2021ycjh-bgzxm0139, and is supported by the 111 Project D21024

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  1. School of Mathematical Sciences, Chongqing Normal University, Chongqing, 401331, China

    Shuwen Chen & Fangyang Zheng

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  1. Shuwen Chen
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  2. Fangyang Zheng
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Chen, S., Zheng, F. On Strominger Space Forms. J Geom Anal 32, 141 (2022). https://doi.org/10.1007/s12220-022-00882-7

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  • DOI: https://doi.org/10.1007/s12220-022-00882-7

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