Surfaces in the lightlike cone
type: Item
instance of: scholarly article
title: Surfaces in the lightlike cone
zbMATH Open document ID: 1108.53011
author: Huili Liu
published in: Journal of Mathematical Analysis and Applications
publication date: 2006-12-07T00:00:00Z
review text: Let \(E^{n+1}_q\) be \(n+1\)-dimensional pseudo-Riemannian space with pseudo-Riemannian metric \(\bar{G}\). It is well known that the pseudo-Riemannian light-like cone (or quadric cone) is defined by \(Q^{n}_{q}(c)=\{x \in E^{n+1}_q \mid \overline{G}(x-c, x-c)=0\}\). Since \(Q^{n}_{q}(c)\) is a degenerate hypersurface in \(E^{n+1}_q\), studying the geometry of such surfaces is harder than the other cases: space-like and time-like surfaces. In this interesting paper, the author obtains the structure equations and their integrability conditions for a surface with isothermal parameters in the lihgt-like cone \(Q^{n}\) (for \(c=0\) and \(q=1)\), and then classifies certain homogeneous surfaces in 3 and 4-dimensional cones \(Q^{3}\) and \(Q^{4}\).
Mathematics Subject Classification ID: 53B25
Mathematics Subject Classification ID: 53B30
zbMATH DE Number: 5078883
zbMATH Keywords: light-like cone
zbMATH Keywords: conformal invariant
zbMATH Keywords: homogeneous surface
reviewed by: Kazim İlarslan
MaRDI profile type: Publication
full work available at URL: j.jmaa.2006.02.064
OpenAlex ID: W2002216846
cites work: Conformally Flat Riemannian Manifolds as Hypersurfaces of the Light Cone
cites work: Möbius isoparametric hypersurfaces in \(S^{n+1}\) with two distinct principal curvatures
cites work: Möbius isotropic submanifolds in \(\mathbb{S}^n\)
cites work: Q3312869
cites work: Moebius geometry of submanifolds in \(\mathbb{S}^n\)
DOI: 10.1016/J.JMAA.2006.02.064
description: scientific article; zbMATH DE number 5078883