Classification of Laguerre isoparametric hypersurfaces in

Let be an ‐dimensional hypersurface in and be the Laguerre second fundamental form of the immersion x. An eigenvalue of Laguerre second fundamental form is called a Laguerre principal curvature of x. An umbilic free hypersurface with non‐zero principal curvatures and vanishing Laguerre form is called a Laguerre isoparametric hypersurface if the Laguerre principal curvatures of x are constants. In this paper, we obtain a complete classification for all oriented Laguerre isoparametric hypersurfaces in .