Abstract: Let x:Mn→Ln+1 be an isometric immersion of Riemannian manifold Mn into the Minkowski space Ln+1.The map x~=xxT (T denotes transpose) is called the quadric representation of the spacelike hypersurface Mn.We study the hypersurface Mn which satisfies □x~=Bx~+C,where □ is the linearized operator of the mean curvature of hypersurface Mn,B and C are two constant matrices.

Key words: spacelike hypersurface, quadric representation, mean curvature, linearized operator