Levi-Civita Ricci-flat metrics on compact complex manifolds

The Journal of Geometric Analysis（2019）

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摘要

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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关键词

Levi-Civita connection,Ricci flat,Classification

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