Spacelike Dupin hypersurfaces in Lorentzian space forms
type: Item
instance of: scholarly article
title: Spacelike Dupin hypersurfaces in Lorentzian space forms
zbMATH Open document ID: 1404.53014
author: Tongzhu Li
author: Changxiong Nie
published in: Journal of the Mathematical Society of Japan
publication date: 2018-07-12T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.jmsj/1524038664
review text: In this paper, a \textit{Dupin hypersurface} in the Lorentz space form \(M_1^{n+1} (c)\) is defined as follows: Consider a space-like hypersurface \(x:M^n \to M_1^{n+1} (c)\) and define a \textit{curvature surface} of \(M^n\) as a smooth connected submanifold \(S\) such that for each point \(p\in S\), the tangent space \(T_p(S)\) is equal to a principal space of the shape operator \(\mathcal{A}\) of \(M^n\) at \(p\). The hypersurface \(M^n\) is then called a Dupin hypersurface if along each curvature surface the associated principal curvature is constant. In the paper under review, the authors study space-like Dupin hypersurfaces from the point of view of conformal geometry. They give a local classification of such surfaces with constant Möbius curvatures, after showing that the Möbius curvatures are invariant under conformal transformations of \(M_1^{n+1} (c)\).
reviewed by: Athanase Papadopoulos
Mathematics Subject Classification ID: 53A30
Mathematics Subject Classification ID: 53C50
zbMATH DE Number: 6902432
zbMATH Keywords: Dupin hypersurface
zbMATH Keywords: principal curvatures
zbMATH Keywords: Möbius curvatures
MaRDI profile type: Publication
OpenAlex ID: W2801983794
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Wikidata QID: Q129951561
DOI: 10.2969/JMSJ/07027573
description: scientific article; zbMATH DE number 6902432