Laguerre Isopararmetric Hypersurfaces in R^4

Let x ： M →R^n be an umbilical free hypersurface with non-zero principal curvatures. Then x is associated with a Laguerre metric g, a Laguerre tensor L, a Laguerre form C, and a Laguerre second fundamental form B which are invariants of x under Laguerre transformation group. A hypersurface x is call...

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Bibliographic Details
Published in数学学报：英文版 Vol. 28; no. 6; pp. 1179 - 1186
Main Author Tong Zhu LI Hua Fei SUN
Format Journal Article
LanguageEnglish
Published 2012
Subjects
主曲率
变换群
特征值
第二基本形式
等参数
等参超曲面
自由曲面
非零
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Summary:Let x ： M →R^n be an umbilical free hypersurface with non-zero principal curvatures. Then x is associated with a Laguerre metric g, a Laguerre tensor L, a Laguerre form C, and a Laguerre second fundamental form B which are invariants of x under Laguerre transformation group. A hypersurface x is called Laguerre isoparametric if its Laguerre form vanishes and the eigenvalues of B are constant. In this paper, we classify all Laguerre isoparametric hypersurfaces in R^4.
Bibliography:Laguerre transformation group, Laguerre isoparametric hypersurface, Laguerre second fundamental form
11-2039/O1
Let x ： M →R^n be an umbilical free hypersurface with non-zero principal curvatures. Then x is associated with a Laguerre metric g, a Laguerre tensor L, a Laguerre form C, and a Laguerre second fundamental form B which are invariants of x under Laguerre transformation group. A hypersurface x is called Laguerre isoparametric if its Laguerre form vanishes and the eigenvalues of B are constant. In this paper, we classify all Laguerre isoparametric hypersurfaces in R^4.
ISSN:1439-8516
1439-7617