单位球面上的子流形有关截曲率的Pinching定理被引量：1

The Pinching Theorems about Sectional Curvature of Submanifolds on Unit Sphere

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摘要设M是单位球面上不含脐点的子流形,Moebius形式Φ消失,本文讨论M 关于Mobius度量的截曲率的Pinching问题. Let M be a submanifold without umbilic point on unit sphere; its Moebius form Φ vanishes, in this paper the pinching theorems of sectional curvature about Moebius metric are obtained.

作者钟定兴孙弘安吴庆琼

机构地区赣南师范学院数学系

出处《数学学报（中文版）》 SCIE CSCD 北大核心 2003年第1期37-48,共12页 Acta Mathematica Sinica：Chinese Series

基金国家自然科学基金资助项目(10261006) 江西省教委资助项目

关键词单位球面子流形截曲率 PINCHING定理 Moebius metric Sectional curvature Blaschke tensor Moebius second fun-damental form Mobius form

分类号 O186.12 [理学—基础数学]

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参考文献1

1Hai Zhong LI Department of Mathematics, Tsinghua University. Beijing 100084. P. R. China Hui Li LIU Department of Mathematics, Northeastern University. Shenyang 110000. P. R. China Chang Ping WANG Key Laboratory of Pure and Applied Mathematics, School of Mathematical Sciences. Peking University, Beijing 100871, P. R. China Guo Song ZHAO Department of Mathematics, Sichuan University, Chengdu 610064. P. R. China.Mobius Isoparametric Hypersurfaces in S^(n+1) with Two Distinct Principal Curvatures[J].Acta Mathematica Sinica,English Series,2002,18(3):437-446. 被引量：55

二级参考文献3

1Hans Friedrich Münzner.Isoparametrische Hyperfl?chen in Sph?ren[J].Mathematische Annalen.1981(2)
2Hans Friedrich Münzner.Isoparametrische Hyperfl?chen in Sph?ren[J].Mathematische Annalen.1980(1)
3Thomas E. Cecil,Patrick J. Ryan.Focal sets, taut embeddings and the cyclides of Dupin[J].Mathematische Annalen.1978(2)

共引文献54

1HU Zejun,LI Haizhong Department of Mathematics, Zhengzhou University Zhengzhou 450052, China Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China.Classification of hypersurfaces with parallel Mobius second fundamental form in S^(n+1)[J].Science China Mathematics,2004,47(3):417-430. 被引量：34
2NIE ChangXiong 1,2,LI TongZhu 3,HE YiJun 4 & WU ChuanXi 5 1 Faculty of Mathematics and Computer Sciences,Hubei University,Wuhan 430062,China,2 School of Mathematical Sciences,Peking University,Beijing 100871,China,3 Faculty of Sciences,Beijing Institute of Technology,Beijing 100081,China,4 School of Mathematical Sciences,Shanxi University,Taiyuan 030006,China,5 Institute of Mathematics,Hubei University,Wuhan 430062,China.Conformal isoparametric hypersurfaces with two distinct conformal principal curvatures in conformal space[J].Science China Mathematics,2010,53(4):953-965. 被引量：10
3XiaQiaoling.SUBMANIFOLDS IN S^(n+p) WITH PARALLEL MBIUS FORM[J].Applied Mathematics(A Journal of Chinese Universities),2004,19(4):405-416.
4钟定兴,孙弘安.单位球面的超曲面的一个内蕴刚性定理[J].南昌大学学报（理科版）,2005,29(3):208-210. 被引量：1
5舒世昌,刘三阳.S^n中具Moebius平坦法丛的子流形[J].数学学报（中文版）,2005,48(6):1221-1232. 被引量：2
6钟定兴.球面中具有半平行和二阶平行Mbius第二基本形式的超曲面[J].赣南师范学院学报,2006,27(3):21-25.
7Xing Xiao LI Feng Yun ZHANG.Immersed Hypersurfaces in the Unit Sphere S^(m+1) with Constant Blaschke Eigenvalues[J].Acta Mathematica Sinica,English Series,2007,23(3):533-548. 被引量：11
8钟定兴,孙弘安.The Hypersurfaces in a Unit Sphere with Nonnegative Mobius Sectional Curvature[J].Northeastern Mathematical Journal,2007,23(1):15-23.
9宋文彬,冯学尚,汪景琇.太阳表面磁场的分布与演化研究进展[J].天文学进展,2007,25(4):296-304. 被引量：1
10李同柱,孙华飞.S^(n+1)中具有调和M■bius曲率张量的超曲面(英文)[J].数学进展,2008,37(1):57-66.

同被引文献3

1HU Zejun,LI Haizhong Department of Mathematics, Zhengzhou University Zhengzhou 450052, China Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China.Classification of hypersurfaces with parallel Mobius second fundamental form in S^(n+1)[J].Science China Mathematics,2004,47(3):417-430. 被引量：34
2钟定兴.A Formula for Submanifolds in S^n and Its Applications in Moebius Geometry[J].Northeastern Mathematical Journal,2001,17(3):361-370. 被引量：8
3Hai Zhong LI Department of Mathematics, Tsinghua University. Beijing 100084. P. R. China Hui Li LIU Department of Mathematics, Northeastern University. Shenyang 110000. P. R. China Chang Ping WANG Key Laboratory of Pure and Applied Mathematics, School of Mathematical Sciences. Peking University, Beijing 100871, P. R. China Guo Song ZHAO Department of Mathematics, Sichuan University, Chengdu 610064. P. R. China.Mobius Isoparametric Hypersurfaces in S^(n+1) with Two Distinct Principal Curvatures[J].Acta Mathematica Sinica,English Series,2002,18(3):437-446. 被引量：55

引证文献1

1钟定兴,孙弘安,肖卫玲.球面上具有相对仿射共形Gauss映照的超曲面[J].纯粹数学与应用数学,2008,24(1):1-9.

1姬秀,胡传峰.单位球面S^(n+1)中仿Blaschke特征值为常数的超曲面[J].商丘师范学院学报,2014,30(6):24-28.
2钟定兴,孙弘安,张祖锦.S^(n+1)上具有三个互异常仿Blaschke特征值的超曲面[J].数学学报（中文版）,2013,56(5):751-766.
3陈海莲,孙弘安,钟定兴,慕小凯.S^6上仿Blaschke张量的特征值为常数的超曲面[J].南昌大学学报（理科版）,2013,37(2):131-139. 被引量：1
4李兴校,彭业娟.单位球面S^6中的Blaschke等参超曲面[J].中国科学：数学,2010,40(9):881-900. 被引量：2
5李同柱,孙华飞.S^(n+1)中具有调和M■bius曲率张量的超曲面(英文)[J].数学进展,2008,37(1):57-66.

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单位球面上的子流形有关截曲率的Pinching定理被引量：1

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单位球面上的子流形有关截曲率的Pinching定理 被引量：1

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单位球面上的子流形有关截曲率的Pinching定理被引量：1