Yanyan Li and Shichang Shu: Laguerre characterization and rigidity of hypersurfaces in $\mathbb{R}^n$, p.67-79

Abstract:

Let $x: M \rightarrow \mathbb{R}^n$ be an $(n-1)$-dimensional hypersurface in $\mathbb{R}^n$, $\mathbf L$ be the Laguerre tensor, $\mathbf B$ be the Laguerre second fundamental form and ${\mathbf C}$ be the Laguerre form of the immersion $x$. The purpose of this paper is to investigate Laguerre characterization and rigidity of hypersurfaces in $\mathbb{R}^n$. We firstly obtain the classification of Laguerre isoparametric hypersurfaces with three distinct Laguerre principal curvatures one of which is simple and then we obtain a Laguerre rigidity result of hypersurfaces in $\mathbb{R}^n$.

Key Words: Laguerre tensor, Laguerre second fundamental form, Laguerre form, Laguerre metric.

2010 Mathematics Subject Classification: Primary: 53A40;
Secondary: 53B25.

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