On the geometry of maximal spacelike hypersurfaces immersed in a generalized Robertson-Walker spacetime

DOI10.1007/s10231-011-0241-yzbMath1277.53060OpenAlexW2067526282WikidataQ125726448 ScholiaQ125726448MaRDI QIDQ361927

Ulisses L. Parente, Henrique Fernandes de Lima

Publication date: 20 August 2013

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10231-011-0241-y

zbMATH Keywords

space-like hypersurfacenull convergence conditiongeneralized Robertson-Walker space-time

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

Related Items (9)

On the rigidity of complete spacelike hypersurfaces immersed in a generalized Robertson-Walker spacetime ⋮ Unnamed Item ⋮ Spacelike mean curvature flow solitons, polynomial volume growth and stochastic completeness of spacelike hypersurfaces immersed into pp-wave spacetimes ⋮ On the higher order mean curvatures of spacelike hypersurfaces in pp-wave spacetimes ⋮ On the totally geodesic spacelike hypersurfaces in conformally stationary spacetimes ⋮ Complete spacelike hypersurfaces in generalized Robertson-Walker and the null convergence condition: Calabi-Bernstein problems ⋮ New Calabi-Cernstein type results in weighted generalized Robertson-Walker spacetimes ⋮ \(\phi \)-parabolicity and the uniqueness of spacelike hypersurfaces immersed in a spatially weighted GRW spacetime ⋮ Complete spacelike hypersurfaces immersed in pp-wave spacetimes

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Complete foliations of space forms by hypersurfaces
• New examples of entire maximal graphs in \(\mathbb H^2 \times \mathbb R_1\)
• Complete spacelike hypersurfaces with constant mean curvature in \(-\mathbb R\times \mathbb H^n\)
• New characterizations of totally geodesic hypersurfaces in anti-de Sitter space \(\mathbb H^{n+1}_1\)
• Maximal space-like hypersurfaces in the Lorentz-Minkowski spaces
• Uniqueness of spacelike hypersurfaces of constant mean curvature in foliated spacetimes
• Uniqueness of complete spacelike hypersurfaces of constant mean curvature in generalized Robertson-Walker spacetimes
• Stability of hypersurfaces with constant \(r\)-mean curvature
• Complete spacelike hypersurfaces with constant mean curvature in the de Sitter space: a gap theorem
• Maximal spacelike submanifolds of a pseudo-Riemannian space of constant curvature
• Inhomogeneous cosmological models with homogeneous inner hypersurface geometry
• Uniqueness of maximal surfaces in generalized Robertson-Walker spacetimes and Calabi-Bernstein type problems
• On spacelike hypersurfaces of constant sectional curvature Lorentz manifolds
• Isometric immersions of Riemannian manifolds
• On the completeness of nullity foliations
• On the mean curvature of spacelike surfaces in certain three-dimensional Robertson-Walker spacetimes and Calabi-Bernstein's type problems
• Complete spacelike hypersurfaces in a Robertson–Walker spacetime
• Harmonic functions on complete riemannian manifolds
• Uniqueness of spacelike hypersurfaces with constant higher order mean curvature in generalized Robertson–Walker spacetimes
• The Large Scale Structure of Space-Time
• Constant mean curvature spacelike surfaces in three-dimensional generalized Robertson-Walker spacetimes

This page was built for publication: On the geometry of maximal spacelike hypersurfaces immersed in a generalized Robertson-Walker spacetime