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RICCI CURVATURES ON HERMITIAN MANIFOLDS
Liu, Kefeng1,2; Yang, Xiaokui3,4
2017-07-01
Source PublicationTRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN0002-9947
Volume369Issue:7Pages:5157-5196
AbstractIn this paper, we introduce the first Aeppli-Chern class for complex manifolds and show that the (1, 1)-component of the curvature 2-form of the Levi-Civita connection on the anti-canonical line bundle represents this class. We systematically investigate the relationship between a variety of Ricci curvatures on Hermitian manifolds and the background Riemannian manifolds. Moreover, we study non-Kahler Calabi-Yau manifolds by using the first Aeppli-Chern class and the Levi-Civita Ricci-flat metrics. In particular, we construct explicit Levi-Civita Ricci-flat metrics on Hopf manifolds S2n-1 x S-1. We also construct a smooth family of Gauduchon metrics on a compact Hermitian manifold such that the metrics are in the same first Aeppli-Chern class, and their first Chern-Ricci curvatures are the same and non-negative, but their Riemannian scalar curvatures are constant and vary smoothly between negative infinity and a positive number. In particular, it shows that Hermitian manifolds with non-negative first Chern class can admit Hermitian metrics with strictly negative Riemannian scalar curvature.
DOI10.1090/tran/7000
Language英语
Funding ProjectNSF ; China's Recruitment Program of Global Experts and National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000399164000023
PublisherAMER MATHEMATICAL SOC
Citation statistics
Cited Times:11[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/25235
Collection数学所
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, Morningside Ctr Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China
4.Chinese Acad Sci, Hua Loo Keng Key Lab Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Liu, Kefeng,Yang, Xiaokui. RICCI CURVATURES ON HERMITIAN MANIFOLDS[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY,2017,369(7):5157-5196.
APA Liu, Kefeng,&Yang, Xiaokui.(2017).RICCI CURVATURES ON HERMITIAN MANIFOLDS.TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY,369(7),5157-5196.
MLA Liu, Kefeng,et al."RICCI CURVATURES ON HERMITIAN MANIFOLDS".TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 369.7(2017):5157-5196.
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