Some classifications of biharmonic Lorentzian hypersurfaces in Minkowski   5-space $\mathbb E^5_1$
  In this paper, we study Lorentzian hypersurfaces in Minkowski 5-space with non-diagonalizable shape operator whose characteristic polinomial is $(t-k_1)^2(t-k_3)(t-k_4)$ or $(t-k_1)^3(t-k_4)$. We proved that in these cases, a hypersurface is biharmonic if and only if it is minimal. 
Nurettin Cenk Turgay
math.DG