Minimal Complex Surfaces with Levi-Civita Ricci-flat Metrics

doi:10.1007/s10114-018-7340-2

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	Minimal Complex Surfaces with Levi-Civita Ricci-flat Metrics
	Liu, Ke Feng 1,2; Yang, Xiao Kui3
	2018-08-01
发表期刊	ACTA MATHEMATICA SINICA-ENGLISH SERIES
ISSN	1439-8516
卷号	34 期号:8 页码:1195-1207
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 Kahler Calabi-Yau surfaces and Hopf surfaces.
关键词	Levi-Civita Ricci-flat metric kodaira dimension classication
DOI	10.1007/s10114-018-7340-2
语种	英语
资助项目	NSFC[11531012] ; NSFC[11688101]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000441727900001
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/31156
专题	数学所
通讯作者	Liu, Ke Feng
作者单位	1.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
推荐引用方式 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.