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Rigidity Theorem of Hypersurfaces with Constant Scalar Curvature in a Unit Sphere 被引量：2

Rigidity Theorem of Hypersurfaces with Constant Scalar Curvature in a Unit Sphere
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摘要 In this paper, we give a characterization of tori S^1 （ √ nr＋2-n/nr）×S^n-1（√ n-2/nr） and S^m （ √n/m ） ×S^n-m （√n-m/n）. Our result extends the result due to Li （1996）on the condition that M is an n-dimensional complete hypersurface in Sn＋1 with two distinct principal curvatures. Keywords principal curvature, Clifford torus, Gauss equations In this paper, we give a characterization of tori S^1 （ √ nr＋2-n/nr）×S^n-1（√ n-2/nr） and S^m （ √n/m ） ×S^n-m （√n-m/n）. Our result extends the result due to Li （1996）on the condition that M is an n-dimensional complete hypersurface in Sn＋1 with two distinct principal curvatures. Keywords principal curvature, Clifford torus, Gauss equations
作者 Guo Xin WEI
机构地区 Department of Mathematical Sciences
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2007年第6期1075-1082,共8页 数学学报（英文版）
关键词 principal curvature Clifford torus Gauss equations principal curvature, Clifford torus, Gauss equations
分类号 O18 [理学—基础数学]
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参考文献10

  • 1Cheng, S. Y., Yau, S. T.: Hypersurfaces with constant scalar curvature. Math. Ann., 225, 195-204 (1977).
  • 2Li, H.: Hypersurfaces with constant scalar curvature in space forms. Math. Ann., 305, 665-672 (1996).
  • 3Otsuki, T.: Minimal hypersurfaces in a Riemannian manifold of constant curvature. Amer. J. Math., 92, 145-173 (1970).
  • 4Cheng, Q. M.: Hypersurfaces in a unit sphere S^n+1(1) with constant scalar curvature. J. London Math. Soc., 64(2), 755-768 (2001).
  • 5Leite, M. L.: Rotational hypersurfaces of space forms with constant scalar curvature. Manuscripta Math., 67, 285-304 (1990).
  • 6Chern, S. S., do Carmo, M., Kobayashi, S.: Minimal submanifolds of a sphere with second fundamental form of constant length. Funct. Anal. Related Fields., 59-75 (1970).
  • 7Li, H.: Global rigidity theorems of hypersurface. Ark. Math., 35, 327-351 (1997).
  • 8Barbosa, J. N., Brasil Jr., A, Costa, E. A., Lazaro, I. C.: Hypersurfaces of the Euclidean sphere with nonnegative Ricci curvature. Arch. Math. (Basel)., 81(3), 335-341 (2003).
  • 9Cartan, E.: Familles de surfaces isoparametriques dans les espaces a courvure constante. Ann. Mat, 17, 177-191 (1938).
  • 10Lawson, H. B.: Local rigidity theorems for minimal hypersurfaces. Ann. of Math., 89, 179-185 (1969).

引证文献2

Acta Mathematica Sinica,English Series
2007年 第6期

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