LAGUERRE CHARACTERIZATIONS OF HYPERSURFACES IN ℝn

Title & Authors
LAGUERRE CHARACTERIZATIONS OF HYPERSURFACES IN ℝn
Shu, Shichang; Li, Yanyan;

Abstract
Let x : $\small{M{\rightarrow}\mathbb{R}^n}$ be an n - 1-dimensional hypersurface in $\small{\mathbb{R}^n}$, L be the Laguerre Blaschke tensor, B be the Laguerre second fundamental form and $\small{D=L+{\lambda}B}$ be the Laguerre para-Blaschke tensor of the immersion x, where $\small{{\lambda}}$ is a constant. The aim of this article is to study Laguerre Blaschke isoparametric hypersurfaces and Laguerre para-Blaschke isoparametric hypersurfaces in $\small{\mathbb{R}^n}$ 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;
Language
English
Cited by
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