Shichang Shu: Laguerre isoparametric hypersurfaces in $\mathbb{R}^5$, p.211-220

Abstract:

Let $x: M \rightarrow \mathbb{R}^n$ be an $(n-1)$-dimensional hypersurface in $\mathbb{R}^n$ and $\mathbf B$ be the Laguerre second fundamental form of the immersion $x$. An eigenvalue of the Laguerre second fundamental form is called a Laguerre principal curvature of $x$. An umbilic free hypersurface $x: M \rightarrow \mathbb{R}^n$ with non-zero principal curvatures and vanishing Laguerre form $\mathbf {C}\equiv 0$ is called a Laguerre isoparametric hypersurface if the Laguerre principal curvatures of $x$ are constants. The aim of this article is to classify all oriented Laguerre isoparametric hypersurfaces in $\mathbb{R}^5$.

Key Words: Laguerre form, Laguerre second fundamental form, Laguerre metric, Laguerre isoparametric hypersurfaces.

2000 Mathematics Subject Classification: Primary: 53A40;
Secondary: 53B25.

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