舒世昌;曹娟娟;

• 1:咸阳师范学院数学系
• 2:西北大学数学系

摘要(Abstract)：

研究Sⁿ中不含脐点且Moebius形式为零的子流形的Moebius特性.首先得到子流形的Moebius标准数量曲率与截面曲率的一个关系定理,然后分别利用迹为零的Blaschke张量、Moebius标准数量曲率、截面曲率所满足的某种内蕴关系刻画了Sn中不含脐点且Moebius形式为零的子流形的Moebius特性.首先得到子流形的Moebius标准数量曲率与截面曲率的一个关系定理,然后分别利用迹为零的Blaschke张量、Moebius标准数量曲率、截面曲率所满足的某种内蕴关系刻画了Sⁿ中子流形的Moebius特性.

关键词(KeyWords)： Moebius度量;Blaschke张量;Moebius截面曲率;标准数量曲率

Abstract:

Keywords:

基金项目(Foundation): 陕西省自然科学基金(SJ08A31);; 陕西省教育厅专项科研基金(2008JK484)

作者(Authors): 舒世昌;曹娟娟;

参考文献(References)：

• [1]Wang C P.Moebius geometry of submanifolds in S~n[J].Manuscripta Math.,1998,96:517-534.
• [2]Li H Z,Wang C P,Wu F E.A Moebius Characterization of Veronese surfaces in S~n[J].Math.Ann., 2001,319:707-714.
• [3]Li H Z,Wang C P.Surfaces with vanishing Moebius form in S~n[J].Acta.Math.Sinica,English Series, 2003,19(4):671-678.
• [4]Gua Z,Li H Z,Wang C P.The Second variation formula for Willmore submanifolds in S~n[J].Results Math., 2001,40:205-225.
• [5]Liu H L,Wang C P,Zhao G S.Moebius isotropic submanifolds in S~n[J].Tohoku Math.J.,2001,53:553-569.
• [6]Li H Z,Liu H L,Wang C P,et al.Moebius isoparametric hypersurfaces in S~(n+1) with two distinct principal curvatures[J].Acta Mathematica Sinica,English Series,2002,18(3):437-446.
• [7]Hu Zejun,Li H Z.Submanifolds with constant Moebius scalar curvature in S~n[J].Manuccripta math., 2003,111:287-302.
• [8]Zhong D X,Sun H A,Wu Q Q.The pinching theorems about sectional curvature of submanifolds on unit sphere[J].Acta.Mathematica Sinica,2003,46(1):37-48.
• [9]舒世昌,刘三阳.S~n中具Moebius平坦法丛的子流形[J].数学学报,2005,48(6):1221-1232.
• [10]Chern S S,Do Carmo M,Kobayashi S.Minimal submanifolds of a sphere with second fundamental form of constant length[M].New York:Springer,1978.
• [11]Santo S W.Submanifolds with parallel mean curvature vector in shperes[J].Tohoku Math.J.,1994,46:403- 415.
• [12]Chen B Y,Okumure M.Scalar curvature,inequality and submanifold[J].Pro.Amer.Math.Soc.,1973,38: 605-608.