Laguerre isopararmetric hypersurfaces in ℝ 4

Tong Zhu Li; Hua Fei Sun

doi:10.1007/s10114-011-0322-2

Laguerre isopararmetric hypersurfaces in ℝ ⁴

Tong Zhu Li
, Hua Fei Sun

School of Mathematics and Statistics

Beijing Institute of Technology

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	1179-1186
Number of pages	8
Journal	Acta Mathematica Sinica, English Series
Volume	28
Issue number	6
DOIs	https://doi.org/10.1007/s10114-011-0322-2
Publication status	Published - Jun 2012

Keywords

Laguerre isoparametric hypersurface
Laguerre second fundamental form
Laguerre transformation group

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10.1007/s10114-011-0322-2

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AU - Sun, Hua Fei

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N2 - 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.

AB - 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.

KW - Laguerre isoparametric hypersurface

KW - Laguerre second fundamental form

KW - Laguerre transformation group

UR - https://www.scopus.com/pages/publications/84860750973

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JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

IS - 6

ER -

Laguerre isopararmetric hypersurfaces in ℝ ⁴

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Keywords

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