Levi-Civita Ricci-flat metrics on compact complex manifolds

2018/06/18 by Jie He, Kefeng Liu, He, Jie +3 · 1 citation
Mathematics · #53C55 #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1806.07206

openalex publication_date 2018/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 Kahler Calabi-Yau surfaces or Hopf surfaces.

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• Comparison theorems in Hermitian geometry I

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