Biharmonic hypersurfaces in space forms with three distinct principal curvatures

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In this paper, we have studied biharmonic hypersurfaces in space form Mⁿ⁺¹(c) with constant sectional curvature c. We have obtained that biharmonic hypersurfaces Mⁿ with at most three distinct principal curvatures in Mⁿ⁺¹(c) has constant mean curvature. We also obtain the full classification of biharmonic hypersurfaces with at most three distinct principal curvatures in arbitrary dimension space form Mⁿ⁺¹(c).