Complete hypersurfaces with constant Laguerre scalar curvature in \(\mathbb R^n\) (Q296176)

The supremum of the absolute trace-free Laguerre tensor over a complete, umbilic free hypersurface in \(\mathbb R^n\), \(n > 3\), with non-zero principal curvatures, vanishing Laguerre form, and constant normalized Laguerre scalar curvature \(R\) is bounded from below by \(\sqrt{(n-1)(n-2)}R/((n-1)(n-2)(n-3))\). If this supremum is zero, the hypersurface is Laguerre equivalent to a Laguerre isotropic hypersurface. If the supremum is greater than zero and actually attained, the hypersurface is Laguerre equivalent to a certain embedding of \(H_1 \times S^{n-2}\) into \(\mathbb R^n\).