Surfaces with Vanishing Moebius Form in S^n 被引量：26

Surfaces with Vanishing Moebius Form in S^n

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摘要 An important Moebius invariant in the theory of Moebius surfaces in S^n inthe so-called Moebius form. In this paper, we give a complete classification of surfaces in S^n withvanishing Moebius form under the Moebius transformation group. An important Moebius invariant in the theory of Moebius surfaces in S^n inthe so-called Moebius form. In this paper, we give a complete classification of surfaces in S^n withvanishing Moebius form under the Moebius transformation group.

作者 HaiZhongLI ChangPingWANG

机构地区 DepartmentofMathematicalSciences SchoolofMathematicalSciences(LMAM)

出处《Acta Mathematica Sinica,English Series》 SCIE CSCD 2003年第4期671-678,共8页 数学学报（英文版）

关键词 conformal invariants Moebius form minimal surfaces conformal invariants Moebius form minimal surfaces

分类号 O152 [理学—基础数学]

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相关文献

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

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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,LI TongZhu,HE YiJun,WU ChuanXi.Conformal isoparametric hypersurfaces with two distinct conformal principal curvatures in conformal space[J].Science China Mathematics,2010,53(4):953-965.
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：2
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.
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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25

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,LI TongZhu,HE YiJun,WU ChuanXi.Conformal isoparametric hypersurfaces with two distinct conformal principal curvatures in conformal space[J].Science China Mathematics,2010,53(4):953-965.
3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
4吴连发.S^3中具有半平行Moebius第二基本形式的曲面[J].上饶师范学院学报,2006,26(6):11-14. 被引量：1
5Xing 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
6钟定兴,孙弘安.单位球面上仿Blaschke张量的特征值为常数的超曲面[J].数学学报（中文版）,2008,51(3):579-592. 被引量：5
7聂昌雄,吴传喜.共形空间中平行的共形第二基本形式的类空超曲面[J].数学学报（中文版）,2008,51(4):685-692. 被引量：9
8聂昌雄,吴传喜.共形空间中的正则子流形[J].数学年刊（A辑）,2008,29(3):315-324. 被引量：4
9Xing Xiao LI Feng Yun ZHANG.On the Blaschke Isoparametric Hypersurfaces in the Unit Sphere[J].Acta Mathematica Sinica,English Series,2009,25(4):657-678. 被引量：12
10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

引证文献26

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
3Tong Zhu LI.Laguerre Geoinetry of Surfaces in R^3[J].Acta Mathematica Sinica,English Series,2005,21(6):1525-1534. 被引量：4
4夏巧玲.关于具有常平均曲率和数量曲率超曲面的Mbius几何的一个注记[J].数学进展,2006,35(6):677-684. 被引量：1
5Xing 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
6聂昌雄,吴传喜.共形空间中平行的共形第二基本形式的类空超曲面[J].数学学报（中文版）,2008,51(4):685-692. 被引量：9
7聂昌雄,吴传喜.共形空间中的正则子流形[J].数学年刊（A辑）,2008,29(3):315-324. 被引量：4
8Zhen GUO.Higher Order Willmore Hypersurfaces in Euclidean Space[J].Acta Mathematica Sinica,English Series,2009,25(1):77-84. 被引量：3
9Xing Xiao LI Feng Yun ZHANG.On the Blaschke Isoparametric Hypersurfaces in the Unit Sphere[J].Acta Mathematica Sinica,English Series,2009,25(4):657-678. 被引量：12
10Ze Jun HU,Xiao Li TIAN.On Mbius Form and Mbius Isoparametric Hypersurfaces[J].Acta Mathematica Sinica,English Series,2009,25(12):2077-2092. 被引量：1

二级引证文献59

1NIE ChangXiong,LI TongZhu,HE YiJun,WU ChuanXi.Conformal isoparametric hypersurfaces with two distinct conformal principal curvatures in conformal space[J].Science China Mathematics,2010,53(4):953-965.
2李兴校,张凤云.单位球面S^(m+1)中具有平行Blaschke张量的超曲面的完全分类[J].河南师范大学学报（自然科学版）,2005,33(3):183-183.
3吴连发.S^3中具有半平行Moebius第二基本形式的曲面[J].上饶师范学院学报,2006,26(6):11-14. 被引量：1
4Xing 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
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.
6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.
7钟定兴,孙弘安.单位球面上仿Blaschke张量的特征值为常数的超曲面[J].数学学报（中文版）,2008,51(3):579-592. 被引量：5
8聂昌雄,吴传喜.共形空间中平行的共形第二基本形式的类空超曲面[J].数学学报（中文版）,2008,51(4):685-692. 被引量：9
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10Zhen GUO.Higher Order Willmore Hypersurfaces in Euclidean Space[J].Acta Mathematica Sinica,English Series,2009,25(1):77-84. 被引量：3

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Acta Mathematica Sinica,English Series

2003年第4期

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