Minimal Complex Surfaces with Levi-Civita Ricci-flat Metrics | |
Liu, Ke Feng1,2; 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. |
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