Characterization of null cones under a Ricci curvature condition
type: Item
instance of: scholarly article
title: Characterization of null cones under a Ricci curvature condition
zbMATH Open document ID: 1486.53025
author: Manuel Gutiérrez
author: Benjamín Olea
published in: Journal of Mathematical Analysis and Applications
publication date: 2022-01-21T00:00:00Z
review text: Null hypersurfaces arise in a natural way in Lorentzian geometry and they have no Riemannian counterpart. It is not easy to study them due to the fact that the induced metric is degenerate, so it is important to develop ideas and tools to get a best understanding on their geometry and topology. This paper is devoted to the study of the conditions under which a totally umbilic immersed null hypersurface in a Lorentzian manifold is contained in a null cone. The main tool used for this purpose is the rigging technique and the analysis of the Raychaudhuri equation for an immersed null hypersurface. Conditions to ensure that the null conjugate locus is a single point and the existence of two vertices in a null cone are also given.
reviewed by: M. Ferreiro-Subrido
Mathematics Subject Classification ID: 53B25
Mathematics Subject Classification ID: 53B30
zbMATH DE Number: 7461319
zbMATH Keywords: immersed null hypersurface
zbMATH Keywords: null cone
zbMATH Keywords: rigging technique
zbMATH Keywords: null conjugate locus
zbMATH Keywords: null Raychaudhuri equation
MaRDI profile type: Publication
full work available at URL: j.jmaa.2021.125906
OpenAlex ID: W4200194039
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DOI: 10.1016/J.JMAA.2021.125906
description: scientific article; zbMATH DE number 7461319