SPACELIKE HYPERSURFACES IN RIEMANNIAN OR LORENTZIAN SPACE FORMS SATISFYING Lkx = Ax plus b

被引:0
作者
Pashaie, F. [1 ]
Kashani, S. M. B. [1 ]
机构
[1] Tarbiat Modares Univ, Fac Math Sci, Dept Pure Math, Tehran, Iran
关键词
Linearized operator L-k; higher order mean curvatures; Lorentzian space forms; EXTENSION;
D O I
暂无
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We study connected orientable spacelike hypersurfaces x : M-n -> M-q(n+1)(c), isometrically immersed into the Riemannian or Lorentzian space forms of curvature c = -1,0,1, and index q = 0, 1, satisfying the condition L(k)x = Ax + b, where L-k is the linearized operator of the (k + 1)th mean curvature Hk+1 of the hypersurface for a fixed integer 0 <= k < n, A is a constant matrix and b is a constant vector. We show that the only hypersurfaces satisfying that condition are hypersurfaces with zero Hk+1 and constant H-k (when c not equal 0), open pieces of totally umbilic hypersurfaces and open pieces of the standard Riemannian product of two totally umbilic hypersurfaces.
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页码:205 / 223
页数:19
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