Spacelike Dupin hypersurfaces in Lorentzian space forms

Tongzhu Li; Changxiong Nie

doi:10.2969/jmsj/07027573

Spacelike Dupin hypersurfaces in Lorentzian space forms

Tongzhu Li, Changxiong Nie

School of Mathematics and Statistics

Hubei University

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

8 Citations (Scopus)

Abstract

Similar to the definition in Riemannian space forms, we define the spacelike Dupin hypersurface in Lorentzian space forms. As conformal invariant objects, spacelike Dupin hypersurfaces are studied in this paper using the framework of the conformal geometry of spacelike hypersurfaces. Further we classify the spacelike Dupin hypersurfaces with constant Möbius curvatures, which are also called conformal isoparametric hypersurface.

Original language	English
Pages (from-to)	463-480
Number of pages	18
Journal	Journal of the Mathematical Society of Japan
Volume	70
Issue number	2
DOIs	https://doi.org/10.2969/jmsj/07027573
Publication status	Published - 2018

Keywords

Conformal isoparametric hypersurface
Dupin hypersurface
Möbius curvatures
Principal curvatures

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10.2969/jmsj/07027573

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abstract = "Similar to the definition in Riemannian space forms, we define the spacelike Dupin hypersurface in Lorentzian space forms. As conformal invariant objects, spacelike Dupin hypersurfaces are studied in this paper using the framework of the conformal geometry of spacelike hypersurfaces. Further we classify the spacelike Dupin hypersurfaces with constant M{\"o}bius curvatures, which are also called conformal isoparametric hypersurface.",

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AU - Nie, Changxiong

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AB - Similar to the definition in Riemannian space forms, we define the spacelike Dupin hypersurface in Lorentzian space forms. As conformal invariant objects, spacelike Dupin hypersurfaces are studied in this paper using the framework of the conformal geometry of spacelike hypersurfaces. Further we classify the spacelike Dupin hypersurfaces with constant Möbius curvatures, which are also called conformal isoparametric hypersurface.

KW - Conformal isoparametric hypersurface

KW - Dupin hypersurface

KW - Möbius curvatures

KW - Principal curvatures

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Spacelike Dupin hypersurfaces in Lorentzian space forms

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Keywords

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