# LAGUERRE CHARACTERIZATIONS OF HYPERSURFACES IN ℝn

Shu, Shichang;Li, Yanyan

• Published : 2013.11.30
• 21 6

#### Abstract

Let x : $M{\rightarrow}\mathbb{R}^n$ be an n - 1-dimensional hypersurface in $\mathbb{R}^n$, L be the Laguerre Blaschke tensor, B be the Laguerre second fundamental form and $D=L+{\lambda}B$ 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

#### References

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