Classification of proper biharmonic hypersurfaces in pseudo-Riemannian space forms

In this paper, we give some examples of proper biharmonic hypersurfaces in de Sitter space Sqn+1(c) and anti-de Sitter space Hqn+1(c), and prove a classification theorem of nondegenerate proper biharmonic hypersurfaces with diagonalizable shape operator and at most two distinct principal curvatures in pseudo-Riemannian space forms Nqn+1(c).