Totally umbilical lightlike hypersurfaces in Robertson-Walker spacetimes
type: Item
instance of: scholarly article
title: Totally umbilical lightlike hypersurfaces in Robertson-Walker spacetimes
zbMATH Open document ID: 1293.53019
DOI: 10.1155/2014/974695
author: Junhong Dong
author: Ximin Liu
published in: ISRN Geometry
publication date: 2014-06-16T00:00:00Z
review text: Summary: We study the problem of light-like hypersurfaces immersed into Robertson-Walker (RW) space-times, where the screen bundle of the hypersurface has constant higher-order mean curvature. We consider the following question: Under what conditions is the compact light-like hypersurface totally umbilical? Our approach is based on the relationship between the light-like hypersurface with its screen bundle and the Minkowski formulae for the screen bundle.
Mathematics Subject Classification ID: 53B25
Mathematics Subject Classification ID: 53Z05
Mathematics Subject Classification ID: 53B30
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 6304710
zbMATH Keywords: screen bundle
zbMATH Keywords: constant higher-order mean curvature
zbMATH Keywords: totally umbilical
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/974695
OpenAlex ID: W2011802049
Wikidata QID: Q59049111
cites work: Maximal space-like hypersurfaces in the Lorentz-Minkowski spaces
cites work: Isolated maximal surfaces in spacetime
cites work: Q4098330
cites work: On maximal surfaces in asymptotically flat space-times
cites work: H-surfaces in Lorentzian manifolds
cites work: Some remarks on the existence of spacelike hypersurfaces of constant mean curvature
cites work: Q4271943
cites work: INTEGRAL FORMULAE FOR SPACELIKE HYPERSURFACES IN CONFORMALLY STATIONARY SPACETIMES AND APPLICATIONS
cites work: Uniqueness of spacelike hypersurfaces with constant higher order mean curvature in generalized Robertson–Walker spacetimes
cites work: Q4874385
cites work: Lightlike hypersurfaces of Lorentzian manifolds with distinguished screen
cites work: Q3833208
cites work: Uniqueness of complete spacelike hypersurfaces of constant mean curvature in generalized Robertson-Walker spacetimes
cites work: Spacelike hypersurfaces of constant mean curvature and Calabi-Bernstein type problems
cites work: Some integral formulas for closed hypersurfaces
cites work: Integral Formulas and Hyperspheres in a Simply Connected Space Form
description: scientific article; zbMATH DE number 6304710