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Some recent progress in non-Kähler geometry

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Abstract

In this paper, we discuss some recent progress in the study of non-Kähler manifolds, in particular the Hermitian geometry of flat canonical connections and Kähler-like connections. We also discuss a number of conjectures and open questions in this direction.

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Acknowledgements

The author thanks his former coauthors Gabriel Khan, Luigi Vezzoni, Qingsong Wang, Bo Yang, and Quanting Zhao for their collaborations. The survey is based on the joint works with them.

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Authors and Affiliations

  1. Department of Mathematics, The Ohio State University, Columbus, OH, 43210, USA

    Fangyang Zheng

  2. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China

    Fangyang Zheng

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  1. Fangyang Zheng
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Correspondence to Fangyang Zheng.

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Dedicated to Professor Lo Yang on the Occasion of His 80th Birthday

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Zheng, F. Some recent progress in non-Kähler geometry. Sci. China Math. 62, 2423–2434 (2019). https://doi.org/10.1007/s11425-019-9528-1

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