Laguerre characterizations of hypersurfaces in $\mathbb{R}^n$
Bull. Korean Math. Soc. 2013 Vol. 50, No. 6, 1781-1797
https://doi.org/10.4134/BKMS.2013.50.6.1781
Published online November 1, 2013
Shichang Shu and Yanyan Li
Xianyang Normal University, Xianyang Normal University
Abstract : 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
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