Complete hypersurfaces immersed in a semi-Riemannian warped product

DOI10.1016/j.difgeo.2011.11.010zbMath1238.53035OpenAlexW2067413273WikidataQ115356743 ScholiaQ115356743MaRDI QIDQ763061

Joseílson R. De Lima, Henrique Fernandes de Lima

Publication date: 8 March 2012

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.difgeo.2011.11.010

zbMATH Keywords

immersionscomplete hypersurfacessemi-Riemannian warped product spacesslices

Mathematics Subject Classification ID

Applications of differential geometry to physics (53Z05) General relativity (83C99) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Local Riemannian geometry (53B20)

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On complete spacelike hypersurfaces in a semi-Riemannian warped product ⋮ Eigenvalue estimates for the stability operator of CMC compact surfaces in three-dimensional warped products ⋮ Rigidity and nonexistence of complete hypersurfaces via Liouville type results and other maximum principles, with applications to entire graphs ⋮ On the angle of complete hypersurfaces in semi-Riemannian product spaces ⋮ Curvature estimates for graphs in warped product spaces ⋮ Sharp estimates for the first stability eigenvalue of surfaces in the presence of a closed conformal vector field ⋮ Uniqueness of entire graphs in Riemannian warped products ⋮ On the first stability eigenvalue of CMC surfaces into warped products with two-dimensional fiber

Cites Work

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• The geometry of closed conformal vector fields on Riemannian spaces
• Some rigidity theorems in semi-Riemannian warped products
• On the rigidity of constant mean curvature complete vertical graphs in warped products
• A nonlinear inequality arising in geometry and Calabi-Bernstein type problems
• On spacelike hypersurfaces with constant mean curvature in the de Sitter space
• 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
• Spacelike hypersurfaces of constant mean curvature and Calabi-Bernstein type problems
• Uniqueness of maximal surfaces in generalized Robertson-Walker spacetimes and Calabi-Bernstein type problems
• Isometric immersions of Riemannian manifolds
• On the mean curvature of spacelike surfaces in certain three-dimensional Robertson-Walker spacetimes and Calabi-Bernstein's type problems
• Bernstein-type theorems in semi-Riemannian warped products
• Complete spacelike hypersurfaces in a Robertson–Walker spacetime
• Spacelike hypersurfaces of constant higher order mean curvature in generalized Robertson–Walker spacetimes
• CONSTANT HIGHER-ORDER MEAN CURVATURE HYPERSURFACES IN RIEMANNIAN SPACES
• Harmonic functions on complete riemannian manifolds
• Unicity of constant mean curvature hypersurfaces in some riemannian manifolds
• INTEGRAL FORMULAE FOR SPACELIKE HYPERSURFACES IN CONFORMALLY STATIONARY SPACETIMES AND APPLICATIONS
• Hypersurfaces of constant higher order mean curvature in warped products
• Uniqueness of spacelike hypersurfaces with constant higher order mean curvature in generalized Robertson–Walker spacetimes
• The Large Scale Structure of Space-Time
• Spacelike hypersurfaces with constant mean curvature in the steady state space
• Constant mean curvature spacelike surfaces in three-dimensional generalized Robertson-Walker spacetimes