Möbius curvature, Laguerre curvature and Dupin hypersurface

Tongzhu Li; Jie Qing; Changping Wang

doi:10.1016/j.aim.2017.02.024

Möbius curvature, Laguerre curvature and Dupin hypersurface

Tongzhu Li^*, Jie Qing, Changping Wang

^*此作品的通讯作者

数学学院

科研成果: 期刊稿件 › 文章 › 同行评审

10 引用（Scopus）

摘要

In this paper we show that a Dupin hypersurface with constant Möbius curvatures is Möbius equivalent to either an isoparametric hypersurface in the sphere or a cone over an isoparametric hypersurface in a sphere. We also show that a Dupin hypersurface with constant Laguerre curvatures is Laguerre equivalent to a flat Laguerre isoparametric hypersurface. These results solve the major issues related to the conjectures of Cecil et al. on the classification of Dupin hypersurfaces.

源语言	英语
页（从-至）	249-294
页数	46
期刊	Advances in Mathematics
卷	311
DOI	https://doi.org/10.1016/j.aim.2017.02.024
出版状态	已出版 - 30 4月 2017

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Li, T., Qing, J., & Wang, C. (2017). Möbius curvature, Laguerre curvature and Dupin hypersurface. Advances in Mathematics, 311, 249-294. https://doi.org/10.1016/j.aim.2017.02.024

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title = "M{\"o}bius curvature, Laguerre curvature and Dupin hypersurface",

abstract = "In this paper we show that a Dupin hypersurface with constant M{\"o}bius curvatures is M{\"o}bius equivalent to either an isoparametric hypersurface in the sphere or a cone over an isoparametric hypersurface in a sphere. We also show that a Dupin hypersurface with constant Laguerre curvatures is Laguerre equivalent to a flat Laguerre isoparametric hypersurface. These results solve the major issues related to the conjectures of Cecil et al. on the classification of Dupin hypersurfaces.",

keywords = "Codazzi tensors, Dupin hypersurfaces, Isoparametric tensors, Laguerre curvatures, M{\"o}bius curvatures",

author = "Tongzhu Li and Jie Qing and Changping Wang",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

year = "2017",

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doi = "10.1016/j.aim.2017.02.024",

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T1 - Möbius curvature, Laguerre curvature and Dupin hypersurface

AU - Li, Tongzhu

AU - Qing, Jie

AU - Wang, Changping

PY - 2017/4/30

Y1 - 2017/4/30

N2 - In this paper we show that a Dupin hypersurface with constant Möbius curvatures is Möbius equivalent to either an isoparametric hypersurface in the sphere or a cone over an isoparametric hypersurface in a sphere. We also show that a Dupin hypersurface with constant Laguerre curvatures is Laguerre equivalent to a flat Laguerre isoparametric hypersurface. These results solve the major issues related to the conjectures of Cecil et al. on the classification of Dupin hypersurfaces.

AB - In this paper we show that a Dupin hypersurface with constant Möbius curvatures is Möbius equivalent to either an isoparametric hypersurface in the sphere or a cone over an isoparametric hypersurface in a sphere. We also show that a Dupin hypersurface with constant Laguerre curvatures is Laguerre equivalent to a flat Laguerre isoparametric hypersurface. These results solve the major issues related to the conjectures of Cecil et al. on the classification of Dupin hypersurfaces.

KW - Codazzi tensors

KW - Dupin hypersurfaces

KW - Isoparametric tensors

KW - Laguerre curvatures

KW - Möbius curvatures

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U2 - 10.1016/j.aim.2017.02.024

DO - 10.1016/j.aim.2017.02.024

M3 - Article

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SN - 0001-8708

VL - 311

SP - 249

EP - 294

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Möbius curvature, Laguerre curvature and Dupin hypersurface

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