Levi-Civita Ricci-flat metrics on compact complex manifolds

Jie He Kefeng Liu Xiaokui Yang

Differential Geometry mathscidoc:1912.43115

The Journal of Geometric Analysis, 1-21, 2020.6
In this paper, we study the geometry of compact complex manifolds with Levi-Civita Ricci-flat metrics and prove that compact complex surfaces admitting Levi-Civita Ricci-flat metrics are Khler Calabi-Yau surfaces or Hopf surfaces.
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@inproceedings{jie2020levi-civita,
  title={Levi-Civita Ricci-flat metrics on compact complex manifolds},
  author={Jie He, Kefeng Liu, and Xiaokui Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111630517317675},
  booktitle={The Journal of Geometric Analysis},
  pages={1-21},
  year={2020},
}
Jie He, Kefeng Liu, and Xiaokui Yang. Levi-Civita Ricci-flat metrics on compact complex manifolds. 2020. In The Journal of Geometric Analysis. pp.1-21. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111630517317675.
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