New characterizations of totally geodesic hypersurfaces in anti-de Sitter space \(\mathbb H^{n+1}_1\)

DOI10.1016/j.geomphys.2010.04.012zbMath1194.53050OpenAlexW2092762772WikidataQ125882344 ScholiaQ125882344MaRDI QIDQ988887

Fernanda Ester Camillo Camargo, Henrique Fernandes de Lima

Publication date: 19 August 2010

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.geomphys.2010.04.012

zbMATH Keywords

second fundamental formscalar curvaturetotally geodesicheight functionLorentzian product spacemaximal spacelike hypersurface

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 (12)

Complete spacelike hypersurfaces in the anti-de Sitter space: rigidity, nonexistence and curvature estimates ⋮ On the geometry of maximal spacelike hypersurfaces immersed in a generalized Robertson-Walker spacetime ⋮ Characterizations of complete spacelike submanifolds in the \((n+p)\)-dimensional anti-de Sitter space of index \(q\) ⋮ Uniqueness and nullity of complete spacelike hypersurfaces immersed in the anti-de Sitter space ⋮ Universal curvature identities. II. ⋮ Curvature properties of spacelike hypersurfaces in a RW spacetime ⋮ On the umbilicity of complete constant mean curvature spacelike hypersurfaces ⋮ On the totally geodesic spacelike hypersurfaces in conformally stationary spacetimes ⋮ Generalized maximum principles and the rigidity of complete spacelike hypersurfaces ⋮ Rigidity results of free boundary maximal hypersurfaces in the region bounded by a de Sitter space ⋮ On the geometry of complete spacelike hypersurfaces in the anti-de Sitter space ⋮ Complete linear Weingarten spacelike submanifolds immersed in the anti-de Sitter space

Cites Work

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• A new characterization of hyperbolic cylinder in anti-de Sitter space \(H_{1}^{n+1} (-1)\)
• New examples of maximal space like surfaces in the anti-de Sitter space
• 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
• Maximal spacelike submanifolds of a pseudo-Riemannian space of constant curvature
• Isometric immersions of Riemannian manifolds
• 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
• General Relativity

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