Hypersurfaces in Esn+1 satisfying ΔH→=λH→ with at most three distinct principal curvatures

In this paper, we investigate hypersurface Mrn of pseudo-Euclidean space Esn+1 satisfying ΔH→=λH→ (λ   a constant), and show that if Mrn has diagonalizable shape operator with at most three distinct principal curvatures, then it has constant mean curvature.