New examples of maximal space like surfaces in the anti-de Sitter space

DOI10.1016/j.jmaa.2008.11.072zbMath1163.83008OpenAlexW2075705127MaRDI QIDQ1014704

Oscar M. Perdomo

Publication date: 29 April 2009

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2008.11.072

zbMATH Keywords

space like surfacesmaximal surfacescomplete surfacesanti-de Sitter spaces

Mathematics Subject Classification ID

Geometrodynamics and the holographic principle (83E05) Applications of differential geometry to physics (53Z05) Special relativity (83A05)

Related Items (9)

Complete spacelike hypersurfaces in the anti-de Sitter space: rigidity, nonexistence and curvature estimates ⋮ On the umbilicity of generalized linear Weingarten spacelike hypersurfaces in a Lorentzian space form ⋮ On the complete spacelike hypersurfaces immersed with two distinct principal curvatures in a locally symmetric Lorentz space ⋮ New characterizations of hyperbolic cylinders in semi-Riemannian space forms ⋮ Uniqueness and nullity of complete spacelike hypersurfaces immersed in the anti-de Sitter space ⋮ CMC hypersurfaces on Riemannian and semi-Riemannian manifolds ⋮ A geometrical correspondence between maximal surfaces in anti-de Sitter space-time and minimal surfaces in \(\mathbb H^2\times\mathbb R\) ⋮ On the complete linear Weingarten spacelike hypersurfaces with two distinct principal curvatures in Lorentzian space forms ⋮ New characterizations of totally geodesic hypersurfaces in anti-de Sitter space \(\mathbb H^{n+1}_1\)

Cites Work

• A new characterization of hyperbolic cylinder in anti-de Sitter space \(H_{1}^{n+1} (-1)\)
• Maximal spacelike submanifolds of a pseudo-Riemannian space of constant curvature
• A congruence theorem for compact spacelike surfaces in de Sitter space

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