摘要
This is a continuation of our previous paper [14]. In [14], we introduced the first Aeppli- Chern class on compact complex manifolds, and proved that the （1, 1） curvature form of the Levi-Civita connection represents the first Aeppli-Chern class which is a natural link between Riemannian geometry and complex geometry. In this paper, we study the geometry of compact complex manifolds with Levi- Civita Ricci-flat metrics and classify minimal complex surfaces with Levi-Civita Ricci-flat metrics. More precisely, we show that minimal complex surfaces admitting Levi-Civita Ricci-flat metrics are K/ihler Calabi-Yau surfaces and Hopf surfaces.
This is a continuation of our previous paper [14]. In [14], we introduced the first Aeppli- Chern class on compact complex manifolds, and proved that the （1, 1） curvature form of the Levi-Civita connection represents the first Aeppli-Chern class which is a natural link between Riemannian geometry and complex geometry. In this paper, we study the geometry of compact complex manifolds with Levi- Civita Ricci-flat metrics and classify minimal complex surfaces with Levi-Civita Ricci-flat metrics. More precisely, we show that minimal complex surfaces admitting Levi-Civita Ricci-flat metrics are K/ihler Calabi-Yau surfaces and Hopf surfaces.
基金
supported in part by NSFC(Grant No.11531012),NSFC(Grant No.11688101)
supported in part by China’s Recruitment Program
