Minimal Complex Surfaces with Levi-Civita Ricci-flat Metrics
Liu, Ke Feng1,2; Yang, Xiao Kui3
AbstractThis 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 Kahler Calabi-Yau surfaces and Hopf surfaces.
KeywordLevi-Civita Ricci-flat metric kodaira dimension classication
Funding ProjectNSFC[11531012] ; NSFC[11688101]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000441727900001
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Document Type期刊论文
Corresponding AuthorLiu, Ke Feng
Affiliation1.Capital Normal Univ, Dept Math, Beijing 100048, Peoples R China
2.Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA
3.Chinese Acad Sci, Acad Math & Syst Sci, Hua Loo Keng Ctr Math Sci, Inst Math,Morningside Ctr Math, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Liu, Ke Feng,Yang, Xiao Kui. Minimal Complex Surfaces with Levi-Civita Ricci-flat Metrics[J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES,2018,34(8):1195-1207.
APA Liu, Ke Feng,&Yang, Xiao Kui.(2018).Minimal Complex Surfaces with Levi-Civita Ricci-flat Metrics.ACTA MATHEMATICA SINICA-ENGLISH SERIES,34(8),1195-1207.
MLA Liu, Ke Feng,et al."Minimal Complex Surfaces with Levi-Civita Ricci-flat Metrics".ACTA MATHEMATICA SINICA-ENGLISH SERIES 34.8(2018):1195-1207.
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