On Laguerre Isopararmetric Hypersurfaces in R7

JI Xiu, HU Chuan-feng

doi:10.13371/j.cnki.chin.q.j.m.2014.04.002

Chinese Quarterly Journal of Mathematics >

2014 , Vol. 29 >Issue 4: 486 - 500

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2014.04.002

On Laguerre Isopararmetric Hypersurfaces in R⁷

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College of Arts and Science, Yangtze University

JI Xiu(1979-), female, native of Xinyang, Henan, a lecturer of Yangtze University, M.S.D., engages in global differential geometry; HU Chuan-feng(1978-), male, native of Xinyang, Henan, a lecturer of Yangtze University, M.S.D., engages in global di®erential geometry and combinatorics and graph theory.

Received date: 2012-10-15

Online published: 2020-11-25

Supported by

Supported by the Department of Education of Hubei Province(B2014281)；

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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, a Laguerre second fundamental form B, which are invariants of x under Laguerre transformation group. A classical theorem of Laguerre geometry states that M（n > 3） is characterized by g and B up to Laguerre equivalence. A Laguerre isopararmetric hypersurface is defined by satisfying the conditions that C = 0 and all the eigenvalues of B with respect to g are constant. It is easy to see that all Laguerre isopararmetric hypersurfaces are Dupin hypersurfaces. In this paper, we established a complete classification for all Laguerre isopararmetric hypersurfaces with three distinct principal curvatures in R⁷.

Key words： laguerre metric; laguerre form; laguerre tensor; laguerre second fundamental form; laguerre isopararmetric hypersurface

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JI Xiu, HU Chuan-feng . On Laguerre Isopararmetric Hypersurfaces in R⁷[J]. Chinese Quarterly Journal of Mathematics, 2014 , 29(4) : 486 -500 . DOI: 10.13371/j.cnki.chin.q.j.m.2014.04.002

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