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

数学学院

Beijing Institute of Technology

科研成果: 期刊稿件 › 文章 › 同行评审

8 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	1179-1186
页数	8
期刊	Acta Mathematica Sinica, English Series
卷	28
期	6
DOI	https://doi.org/10.1007/s10114-011-0322-2
出版状态	已出版 - 6月 2012

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Li, T. Z., & Sun, H. F. (2012). Laguerre isopararmetric hypersurfaces in ℝ ⁴ Acta Mathematica Sinica, English Series, 28(6), 1179-1186. https://doi.org/10.1007/s10114-011-0322-2

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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.

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JO - Acta Mathematica Sinica, English Series

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Laguerre isopararmetric hypersurfaces in ℝ 4

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Laguerre isopararmetric hypersurfaces in ℝ ⁴