Laguerre characterizations of hypersurfaces in $mathbb{R}^n$

摘要

Let $x: M ightarrow mathbb{R}^n$ be an $n-1$-dimensional hypersurface in $mathbb{R}^n$, $mathbf L$ be the Laguerre Blaschke tensor, $mathbf B$ be the Laguerre second fundamental form and ${mathbf D}={mathbf L}+lambda {mathbf B}$ be the Laguerre para-Blaschke tensor of the immersion $x$, where $lambda$ is a constant. The aim of this article is to study Laguerre Blaschke isoparametric hypersurfaces and Laguerre para-Blaschke isoparametric hypersurfaces in $mathbb{R}^n$ with three distinct Laguerre principal curvatures one of which is simple. We obtain some classification results of such isoparametric hypersurfaces.