Classification of hypersurfaces with constant Laguerre eigenvalues in ℝⁿ

Let x: M → ℝⁿ be an umbilical free hypersurface with non-zero principal curvatures. Then x is associated with a Laguerre metric g, a Laguerre tensor L, a Laguerre form C, and a Laguerre second fundamental form B, which are invariants of x under Laguerre transformation group. An eigenvalue of Laguerre tensor L of x is called a Laguerre eigenvalue of x. In this paper, we classify all oriented hypersurfaces with constant Laguerre eigenvalues and vanishing Laguerre form.