子流形与拓扑球面定理(英文) 被引量：1

Submanifolds and the Topological Sphere Theorem

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摘要本文建立了球面Sn+p(c) (c>0 )中的完备子流形的一个拓扑球面定理。 In this paper,we establish a topological sphere theorem for complete submanifolds in a sphere S n+p (c) with c>0,which shows that the topology of a complete submanifold is affected by conditions on the main intrinsic and extrinsic curvature invariants.

作者舒世昌刘三阳

机构地区西安电子科技大学应用数学系

出处《应用数学》 CSCD 北大核心 2004年第1期73-77,共5页 Mathematica Applicata

基金 SupportedbytheNationalNaturalScienceFoundationofChina (6 9972 0 36 ) NSFofShaanxi(0 3JK2 1 5 )

关键词完备子流形拓扑球面定理曲率 RIEMANNIAN流形 Submanifold Topological sphere Fundamental group Homeomorphism

分类号 O189.3 [理学—基础数学]

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同被引文献5

1Cheeger J, Ebin D. Comparsion theorem in Riemannian gromety. New York: North-Holland, 1975.
2Leung P F. Minimal submanifods in a sphere. Math. Z. 1983, 183(1) :75-86.
3Leung P F. An estimate on the Ricci curvature of a submanifold and some applications. Proc. of Amer.Math. Soc. 1992, 114(4):1051-1061.
4Lawson H B, Simons J. On stable currents and their application to global problems in real and complex geometry. Ann. of Math. 1973, 98(3):427-450.
5Sjerve D. Homology spheres which are covered by spheres. J. London Math. Soc. Ser. 1973, 6(2):333-336.

引证文献1

1徐森林,宋冰玉.球面S^(n+p)(c)中子流形的拓扑(英文)[J].数学研究,2005,38(3):238-242.

1王宝富.偶维紧致黎曼流形上关于体积的拓扑球面定理[J].四川大学学报（自然科学版）,1997,34(5):581-583.
2王宝富.径向曲率的一个拓扑球面定理[J].四川大学学报（自然科学版）,1998,35(3):344-347.
3戴文荣.Finsler几何中的一些整体结果[J].复旦学报（自然科学版）,1997,36(2):172-176.

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子流形与拓扑球面定理(英文) 被引量：1

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