Weakly convex hypersurfaces of pseudo-Euclidean spaces satisfying the condition LkHk+1 = λHk+1

In this paper, we try to give a classification of spacelike hypersurfaces the Lorentz-Minkowski space-time E1n+1, whose mean curvature vector field order (k+ 1) is an eigenvector kth linearized operator Lk, for non-negative integer k less than n. The Lk defined as linear part first variation (k + 1)th hypersurface arising from its normal variations. We show that any E1n+1 satisfying condition LkHk+1 = λHk+1 (where 0 ≤ n − belongs class Lk-biharmonic, Lk-1-type or Lk-null-2-type hypersurface. Furthermore, study above on well-known family spaces, named weakly convex (i.e. which all principle curvatures are nonnegative). prove that, (where, r n−1), will be constant. As interesting result, hypersurfaces, having assumed has k-maximal.