Minimal Complex Surfaces with Levi–Civita Ricci-flat Metrics |
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基金项目: | The first author is supported in part by NSFC (Grant No. 11531012); the second auother is supported in part by China's Recruitment Program and NSFC (Grant No. 11688101) |
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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¨ahler Calabi–Yau surfaces and Hopf surfaces.
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