Hypersurfaces In The Euclidean Space Whose Quadric Representations Satisfy L_k(?)=B(?)+C

Let x: Mⁿ→Eⁿ⁺¹ be an orientable hypersurface immersed into the Euclidean space. The map(?)=xx¹ (t denote transpose) is called the quadric representation of Mⁿ. We study the hypersurface in Eⁿ⁺¹ which satisfy L_k(?)=B(?)+C, where L_k is the linearized operator of the (k+1)th mean curvature of hypersurface for a fixed k=0,…, n-1, B and C are two constant matrices. In [5], J. Lu gave some results on submanifolds which satisfyâ–³(?)=B(?)+C. In the present paper we generalize the above results.