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LINEAR WEINGARTEN HYPERSURFACES IN A REAL SPACE FORM

Published online by Cambridge University Press:  25 August 2010

SHICHANG SHU
SHICHANG SHU*
Affiliation:
Department of Mathematics, Xianyang Normal University, Xianyang, Shaanxi 712000, P.R. China e-mail: shushichang@126.com
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Abstract

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In this paper, we investigate linear Weingarten hypersurfaces with two distinct principal curvatures in a real space form Mn+1(c), we obtain two rigidity results and give some characterization of the Riemannian product Sk(a) × Sn−k(), 1 ≤ k ≤ n − 1 in Mn+1(c)(c = 1), the Riemannian product Rk × Sn−k(a), 1 ≤ k ≤ n −1 in Mn+1(c)(c = 0) and the Riemannian product Hk(tanh2 ρ−1) × Sn−k(coth2 ρ−1), 1 ≤ k ≤ n −1 in Mn+1(c)(c = −1).

Keywords

53C4253A10
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue 3 , September 2010 , pp. 635 - 648
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

REFERENCES

1.Cartan, E., Sur des familles remarquables d'hypersurfaces isoparamétriques dans les espaces sphériques, Math. Z. 45 (1939), 335–367.CrossRefGoogle Scholar
2.Cheng, S. Y. and Yau, S. T., Hypersurfaces with constant scalar curvature, Math. Ann. 225 (1977), 195–204.CrossRefGoogle Scholar
3.Cheng, Q. M., Hypersurfaces in a unit sphere S n+1(1) with constant scalar curvature, J. Lond. Math. Soc. 64 (2001), 755–768.CrossRefGoogle Scholar
4.Cheng, Q. M., Complete hypersurfaces in a Euclidean space R n+1 with constant scalar curvature, Indiana Univ. Math. J. 51 (2002), 53–68.CrossRefGoogle Scholar
5.Hu, Z. and Zhai, S., Hypersurfaces of the hyperbolic space with constant scalar curvature, Results Math. 48 (2005), 65–88.CrossRefGoogle Scholar
6.Li, H.. Global rigidity theorems of hypersurfaces, Ark. Mat. 35 (1997), 327–351.CrossRefGoogle Scholar
7.Li, H., Suh, Y. J. and Wei, G., Linear Weingarten hypersurfaces in a unit sphere, Bull. Korean Math. Soc. 46 (2009), 321–329.CrossRefGoogle Scholar
8.Otsuki, T., Minimal hypersurfaces in a Riemannian manifold of constant curvature, Amer. J. Math. 92 (1970), 145–173.CrossRefGoogle Scholar
9.Shu, S. and Yi Han, A., Hypersurfaces in a hyperbolic space with constant k-th mean curvature, Bull. Math. Soc. Sci. Math. Roumanie 52 (100) (2009), 65C78.Google Scholar
10.Shu, S. and Yi Han, A., Nonnegative sectional curvature hypersurfaces in a real space form, Math. Notes 86 (2009), 729–743.CrossRefGoogle Scholar
11.Wei, G., Complete hypersurfaces with constant mean curvature in a unit sphere, Monatsh. Math. 149 (2006), 251–258.CrossRefGoogle Scholar