Minimal complex surfaces with Levi-Civita Ricci-flat metrics
Differential Geometry
2018-08-21 v1
Abstract
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 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\"ahler Calabi-Yau surfaces and Hopf surfaces.
Cite
@article{arxiv.1706.01219,
title = {Minimal complex surfaces with Levi-Civita Ricci-flat metrics},
author = {Kefeng Liu and Xiaokui Yang},
journal= {arXiv preprint arXiv:1706.01219},
year = {2018}
}