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Mean curvature of spacelike submanifolds in a Brinkmann spacetime
dc.contributor.author | Cánovas, Verónica L. | |
dc.contributor.author | Romero, Alfonso | |
dc.contributor.author | Palomo-Ruiz, Francisco José | |
dc.date.accessioned | 2021-09-02T11:17:03Z | |
dc.date.available | 2021-09-02T11:17:03Z | |
dc.date.created | 2021 | |
dc.date.issued | 2021 | |
dc.identifier.uri | https://hdl.handle.net/10630/22781 | |
dc.description.abstract | Several geometric properties of complete spacelike submanifolds, with codimension at least two, in a Brinkmann spacetime are shown from natural assumptions involving the mean curvature vector field $\mcv$ of the spacelike submanifold. Especially, we get sufficient conditions that assure that a spacelike submanifold is contained in a leaf of the foliation of the Brinkmann spacetime defined by the orthogonal vectors to the parallel lightlike vector field. When this vector field is the gradient of a smooth function, a characterization of arbitrary codimension spacelike submanifolds contained in a leaf of this foliation is given. In the case of plane fronted wave spacetimes, relevant examples of Brinkmann spacetimes that generalize pp-waves spacetimes, several uniqueness results for codimension two spacelike submanifolds are obtained. In particular, it is proven that any compact codimension two spacelike submanifold with $\mcv=0$ in a plane fronted spacetime wave must be a (totally geodesic) front of wave. | es_ES |
dc.description.sponsorship | The first author has been partially supported by MINECO/FEDER project MTM2015-65430-P, Fundaci\'on S\'eneca project 19901/GERM/15 and research grant 19783/FPI/15 from Fundaci\'on S\'eneca, the second and the third authors by Spanish MINECO and ERDF project MTM2016-78807-C2-1-P and Andalusian and ERDF project A-FQM-494-UGR18 | es_ES |
dc.language.iso | eng | es_ES |
dc.rights | info:eu-repo/semantics/openAccess | es_ES |
dc.subject | Matemáticas aplicadas | es_ES |
dc.subject | Geometría | es_ES |
dc.subject | Brinkmann | es_ES |
dc.subject.other | Brinkmann spacetime | es_ES |
dc.subject.other | plane fronted wave spacetime, | es_ES |
dc.subject.other | pp-wave spacetime | es_ES |
dc.subject.other | gravitational plane wave spacetime | es_ES |
dc.subject.other | spacelike submanifold, | es_ES |
dc.subject.other | front of wave | es_ES |
dc.subject.other | characteristic hypersurface | es_ES |
dc.subject.other | mean curvature vector field | es_ES |
dc.title | Mean curvature of spacelike submanifolds in a Brinkmann spacetime | es_ES |
dc.type | info:eu-repo/semantics/article | |
dc.centro | Escuela de Ingenierías Industriales | es_ES |
dc.type.hasVersion | info:eu-repo/semantics/submittedVersion | es_ES |