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Levi-Civita Ricci-flat metrics on compact complex manifolds

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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 Kähler Calabi-Yau surfaces or Hopf surfaces.

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Acknowledgements

The second author would like to thank Valentino Tosatti for many useful comments and suggestions. This work was partially supported by China’s Recruitment Program of Global Experts and NSFC 11688101.

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Authors and Affiliations

  1. Academy of Mathematics and System Science, Chinese Academy, Beijing, 100190, China

    Jie He

  2. Department of Mathematics, University of California at Los Angeles, California, 90095, USA

    Kefeng Liu

  3. Morningside Center of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Xiaokui Yang

  4. HCMS, CEMS, NCNIS, HLM, UCAS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Xiaokui Yang

Authors
  1. Jie He
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  2. Kefeng Liu
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  3. Xiaokui Yang
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Correspondence to Xiaokui Yang.

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He, J., Liu, K. & Yang, X. Levi-Civita Ricci-flat metrics on compact complex manifolds. J Geom Anal 30, 646–666 (2020). https://doi.org/10.1007/s12220-019-00156-9

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  • DOI: https://doi.org/10.1007/s12220-019-00156-9

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