Biconservative hypersurfaces in space forms $\overline{M}^{\lowercase{n+1}}(\lowercase{c})$

Abstract

In this paper we study biconservative hypersurfaces $M$ in space forms $\overline M^{n+1}(c)$ with four distinct principal curvatures whose second fundamental form has constant norm. We prove that every such hypersurface has constant mean curvature and constant scalar curvature.