Journal of the Mathematical Society of Japan

Spacelike Dupin hypersurfaces in Lorentzian space forms

Tongzhu LI and Changxiong NIE

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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 Möbius curvatures, which are also called conformal isoparametric hypersurface.

Article information

Source
J. Math. Soc. Japan, Volume 70, Number 2 (2018), 463-480.

Dates
First available in Project Euclid: 18 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1524038664

Digital Object Identifier
doi:10.2969/jmsj/07027573

Mathematical Reviews number (MathSciNet)
MR3787730

Zentralblatt MATH identifier
06902432

Subjects
Primary: 53A30: Conformal differential geometry 53B25: Local submanifolds [See also 53C40]

Keywords
Dupin hypersurface principal curvatures Möbius curvatures conformal isoparametric hypersurface

Citation

LI, Tongzhu; NIE, Changxiong. Spacelike Dupin hypersurfaces in Lorentzian space forms. J. Math. Soc. Japan 70 (2018), no. 2, 463--480. doi:10.2969/jmsj/07027573. https://projecteuclid.org/euclid.jmsj/1524038664


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