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Science China Mathematics

, Volume 62, Issue 11, pp 2423–2434 | Cite as

Some recent progress in non-Kähler geometry

  • Fangyang ZhengEmail author
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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.

Keywords

non-Kähler manifolds Hermitian geometry Kähler-like metrics 

MSC(2010)

53026 53C55 

Notes

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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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsThe Ohio State UniversityColumbusUSA
  2. 2.Department of MathematicsZhejiang Normal UniversityJinhuaChina

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