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CURVATURES OF MODULI SPACE OF CURVES AND APPLICATIONS
Liu, Kefeng1; Sun, Xiaofeng2; Yang, Xiaokui3,4; Yau, Shing-Tung5
2017-10-01
Source PublicationASIAN JOURNAL OF MATHEMATICS
ISSN1093-6106
Volume21Issue:5Pages:841-854
AbstractIn this paper, we investigate the geometry of the moduli space of curves by using the curvature properties of direct image sheaves of vector bundles. We show that the moduli space (M-g, omega wp) of curves with genus g > 1 has dual-Nakano negative and semi-Nakano-negative curvature, and in particular, it has non-positive Riemannian curvature operator and also non-positive complex sectional curvature. We also prove that any submanifold in M-g which is totally geodesic in A(g) with finite volume must be a ball quotient.
KeywordCurvature moduli space Weil-Petersson metric
Language英语
Funding ProjectNSFC[11531012] ; NSFC[11688101] ; China's Recruitment Program
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000424657700003
PublisherINT PRESS BOSTON, INC
Citation statistics
Cited Times:2[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/29568
Collection数学所
Affiliation1.UCLA, Dept Math, Los Angeles, CA 90095 USA
2.Lehigh Univ, Dept Math, Bethlehem, PA 18015 USA
3.Chinese Acad Sci, Acad Math & Syst Sci, Morningside Ctr Math, Beijing, Peoples R China
4.Chinese Acad Sci, Hua Loo Keng Key Lab Math, Acad Math & Syst Sci, Beijing, Peoples R China
5.Harvard Univ, Dept Math, Cambridge, MA 02138 USA
Recommended Citation
GB/T 7714
Liu, Kefeng,Sun, Xiaofeng,Yang, Xiaokui,et al. CURVATURES OF MODULI SPACE OF CURVES AND APPLICATIONS[J]. ASIAN JOURNAL OF MATHEMATICS,2017,21(5):841-854.
APA Liu, Kefeng,Sun, Xiaofeng,Yang, Xiaokui,&Yau, Shing-Tung.(2017).CURVATURES OF MODULI SPACE OF CURVES AND APPLICATIONS.ASIAN JOURNAL OF MATHEMATICS,21(5),841-854.
MLA Liu, Kefeng,et al."CURVATURES OF MODULI SPACE OF CURVES AND APPLICATIONS".ASIAN JOURNAL OF MATHEMATICS 21.5(2017):841-854.
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