Bulletin of the
Korean Mathematical Society BKMS

Let $x: M \rightarrow \mathbb{R}^n$ 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.

Keywords: Laguerre characterization, Laguerre form, Laguerre Blaschke tensor, Laguerre second fundamental form

MSC numbers: 53C42, 53C20