Classification of hypersurfaces with parallel Laguerre second fundamental form in Rn

Tongzhu Li; Haizhong Li; Changping Wang

doi:10.1016/j.difgeo.2009.09.005

Classification of hypersurfaces with parallel Laguerre second fundamental form in Rⁿ

Tongzhu Li^*
, Haizhong Li
, Changping Wang

^*Corresponding author for this work

School of Mathematics and Statistics

Capital Normal University
Tsinghua University
Peking University

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

21 Citations (Scopus)

Abstract

Let x : M → Rⁿ be an umbilical free hypersurface with non-zero principal curvatures. Two basic invariants of x under the Laguerre transformation group are the Laguerre metric g and the Laguerre second fundamental form B. In this paper, we classify all oriented hypersurfaces in Rⁿ with a parallel Laguerre second fundamental form B. Crown

Original language	English
Pages (from-to)	148-157
Number of pages	10
Journal	Differential Geometry and its Application
Volume	28
Issue number	2
DOIs	https://doi.org/10.1016/j.difgeo.2009.09.005
Publication status	Published - Apr 2010

Keywords

Laguerre metric
Laguerre second fundamental form
Laguerre transformation group

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10.1016/j.difgeo.2009.09.005

Cite this

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title = "Classification of hypersurfaces with parallel Laguerre second fundamental form in Rn",

abstract = "Let x : M → Rn be an umbilical free hypersurface with non-zero principal curvatures. Two basic invariants of x under the Laguerre transformation group are the Laguerre metric g and the Laguerre second fundamental form B. In this paper, we classify all oriented hypersurfaces in Rn with a parallel Laguerre second fundamental form B. Crown",

keywords = "Laguerre metric, Laguerre second fundamental form, Laguerre transformation group",

author = "Tongzhu Li and Haizhong Li and Changping Wang",

year = "2010",

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doi = "10.1016/j.difgeo.2009.09.005",

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T1 - Classification of hypersurfaces with parallel Laguerre second fundamental form in Rn

AU - Li, Tongzhu

AU - Li, Haizhong

AU - Wang, Changping

PY - 2010/4

Y1 - 2010/4

N2 - Let x : M → Rn be an umbilical free hypersurface with non-zero principal curvatures. Two basic invariants of x under the Laguerre transformation group are the Laguerre metric g and the Laguerre second fundamental form B. In this paper, we classify all oriented hypersurfaces in Rn with a parallel Laguerre second fundamental form B. Crown

AB - Let x : M → Rn be an umbilical free hypersurface with non-zero principal curvatures. Two basic invariants of x under the Laguerre transformation group are the Laguerre metric g and the Laguerre second fundamental form B. In this paper, we classify all oriented hypersurfaces in Rn with a parallel Laguerre second fundamental form B. Crown

KW - Laguerre metric

KW - Laguerre second fundamental form

KW - Laguerre transformation group

UR - https://www.scopus.com/pages/publications/76849109136

U2 - 10.1016/j.difgeo.2009.09.005

DO - 10.1016/j.difgeo.2009.09.005

M3 - Article

AN - SCOPUS:76849109136

SN - 0926-2245

VL - 28

SP - 148

EP - 157

JO - Differential Geometry and its Application

JF - Differential Geometry and its Application

IS - 2

ER -

Classification of hypersurfaces with parallel Laguerre second fundamental form in Rⁿ

Abstract

Keywords

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