Ricci Curvature and Fundamental Group 被引量：1

Ricci Curvature and Fundamental Group

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摘要 Abstract By refined volume estimates in terms of Ricci curvature, the two results due to J. Milnor （1968） are generalized.

作者 Yuanlong XIN

机构地区 Dedicated to the memory of Shiing-Shen Chern

出处《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2006年第2期113-120,共8页 数学年刊（B辑英文版）

基金 Froject supported by the National Natural Science Foundation of China (No.10531090) the Science Foundation of the Ministry of Education of China.

关键词 Ricci curvature Fundamental group Volume growth Ricci曲率基本原理体积生长几何学

分类号 O18 [理学—基础数学]

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参考文献8

1Bishop,R.L.,A relation between volume,mean curvature,and diameter,Notices Amer.Math.Soc.,10,1963,364.
2Greene,R.E.and Wu,H.,Function theory on manifold which possess a pole,Lecture Notes in Math.,699,Springer-Verlag,1979.
3Gao,L.Z.and Yau,S.-T.,The estimates of negative Ricci curved metrics on three manifolds,Invent.Math.,85,1986,637-652.
4Lohkamp,J.,Metric of negative Ricci curvature,Ann.Math.,140,1994,655-683.
5Milnor,J.,A note on curvature and fundamental group,J.Diff.Geom.,2,1968,1-7.
6Preissman,A.,Quelques proprietes globales des espaces de Riemann,Comment.Math.Helv.,15,1942-43,175-216.
7Xin,Y.L.,Geometry of Harmonic Maps,Birkhauser,1996.
8Yang,Y.-H.,On the growth of fundamental groups on nonpositive curvature manifolds,Bull.Austral.Math.,54,1996,483-487.

同被引文献1

1SHEN YiBing,ZHAO Wei.On fundamental groups of Finsler manifolds In memory of the centenary birthday of Professor S.S.Chern[J].Science China Mathematics,2011,54(9):1951-1964. 被引量：4

引证文献1

1沈一兵,赵唯.关于Finsler流形的曲率与基本群[J].中国科学：数学,2018,48(6):807-818.

1顾会玲.MANIFOLDS WITH POINTWISE PINCHED RICCI CURVATURE[J].Acta Mathematica Scientia,2010,30(3):819-829.
2YANG Fei,SHEN JingFang.Volume growth for gradient shrinking solitons of Ricci-harmonic flow[J].Science China Mathematics,2012,55(6):1221-1228. 被引量：5
3蔡开仁.ESTIMATE ON LOWER BOUND OF THE FIRST EIGENVALUE OF A COMPACT RIEMANNIAN MANIFOLD[J].Chinese Annals of Mathematics,Series B,1991,12(3):267-271. 被引量：3
4THE FUNDAMENTAL GROUP OF THE AUTOMORPHISM GROUP OF A NONCOMMUTATIVE TORUS THE FUNDAMENTAL GROUP OF THE AUTOMORPHISM GROUP OF A NONCOMMUTATIVE TORUS[J].Chinese Annals of Mathematics,Series B,2000,21(4):441-452.
5张易.具有非负Ricci曲率流形的一些拓扑性质[J].大学数学,2016,32(2):8-11.
6Li MA,Anqiang ZHU.Injectivity radius bound of Ricci flow with positive Ricci curvature and applications[J].Frontiers of Mathematics in China,2013,8(5):1129-1137.
7Yong Hua MAO.L^P-Poincaré Inequality for General Symmetric Forms[J].Acta Mathematica Sinica,English Series,2009,25(12):2055-2064. 被引量：1
8Liu JIAN-YU,LIu XI-MIN.Ricci Curvature of Certain Submanifolds in Kenmotsu Space Forms[J].Communications in Mathematical Research,2009,25(4):340-348.
9YIN SongTing,HE Qun,SHEN YiBing.On the first eigenvalue of Finsler manifolds with nonnegative weighted Ricci curvature[J].Science China Mathematics,2014,57(5):1057-1070. 被引量：2
10XU Sen-lin HU Zi-sheng.Small Excess and the Topology of Open Manifolds with Ricci Curvature Negatively Lower Bounded[J].Chinese Quarterly Journal of Mathematics,2007,22(1):16-21.

Chinese Annals of Mathematics,Series B

2006年第2期

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Ricci Curvature and Fundamental Group 被引量：1

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