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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($\sqrt{1-a^2})\$), 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

Information

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

References

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