on biharmonic hypersurfaces of three curvatures in minkowski 5-space

In this paper, we study the lk-biharmonic lorentzian hypersurfaces of the minkowski 5-space m5 , whose second fundamental form has three distinct eigenvalues. an isometrically immersed lorentzian hypersurface, x : m4_1 → m^5 , is said to be lk-biharmonic if it satisfies the condition l 2_kx = 0, where lk is the linearized operator associated to the 1st variation of the mean curvature vector field of order (k + 1) on m4_1 . in the special case k = 0, we have l0 is the well-known laplace operator ∆ and by a famous conjecture due to bang-yen chen each ∆-biharmonic submanifold of every euclidean space is minimal. the conjecture has been affirmed in many riemanian cases. we obtain similar results confirming the lk-conjecture on lorentzian hypersurfaces in m^5 with at least three principal curvatures