Biharmonic hypersurfaces in space forms with three distinct principal curvatures

In this paper, we have studied biharmonic hypersurfaces in space form ${\bar{M}}^{n+1}(c)$ with constant sectional curvature $c$. We have obtained that biharmonic hypersurfaces $M^n$ with at most three distinct principal curvatures in ${\bar{M}}^{n+1}(c)$ 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 ${\bar{M}}^{n+1}(c)$.