On maximal hypersurfaces in Lorentz manifolds admitting a parallel lightlike vector field

We study constant mean curvature spacelike hypersurfaces and in particular maximal hypersurfaces immersed in pp-wave spacetimes satisfying the timelike convergence condition. We prove the non-existence of compact spacelike hypersurfaces whose constant mean curvature is non-zero and also that every c...

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Bibliographic Details
Published inClassical and quantum gravity Vol. 33; no. 5; pp. 55003 - 55010
Main Authors Pelegrín, José A S, Romero, Alfonso, Rubio, Rafael M
Format Journal Article
LanguageEnglish
Published IOP Publishing 03.03.2016
Subjects
Calabi-Bernstein theorem
Constants
Convergence
Curvature
Fields (mathematics)
Geometry
lightlike parallel vector fields
Lorentzian geometry
Manifolds
Mathematical analysis
Quantum gravity
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Summary:We study constant mean curvature spacelike hypersurfaces and in particular maximal hypersurfaces immersed in pp-wave spacetimes satisfying the timelike convergence condition. We prove the non-existence of compact spacelike hypersurfaces whose constant mean curvature is non-zero and also that every compact maximal hypersurface is totally geodesic. Moreover, we give an extension of the classical Calabi-Bernstein theorem to this class of pp-wave spacetimes.
Bibliography:CQG-102205.R1
ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 23
ISSN:0264-9381
1361-6382
DOI:10.1088/0264-9381/33/5/055003