Compact spacelike surfaces in the 3-dimensional de Sitter space with non-degenerate second fundamental form.

DOI10.1016/S0926-2245(03)00019-6zbMath1041.53037WikidataQ115338041 ScholiaQ115338041MaRDI QIDQ1405277

Alfonso Romero, Juan A. Aledo

Publication date: 25 August 2003

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

zbMATH Keywords

second fundamental formde Sitter spaceGaussian curvaturetotally umbilicalcompact spacelike surface

Mathematics Subject Classification ID

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

Related Items (6)

Scalar curvature of spacelike hypersurfaces and certain class of cosmological models for accelerated expanding universes ⋮ A conformal representation for linear Weingarten surfaces in the de Sitter space ⋮ Spacelike surfaces with positive definite second fundamental form in 3D spacetimes ⋮ Some characterizations of totally umbilical surfaces in three-dimensional warped product spaces ⋮ New characterizations of compact totally umbilical spacelike surfaces in 4-dimensional Lorentz-Minkowski spacetime through a lightcone ⋮ On non-degenerate null normal sections of codimension two spacelike surfaces

Cites Work

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• On the Ricci curvature of compact spacelike hypersurfaces in de Sitter space
• Global rigidity theorems of hypersurfaces
• Spacelike hypersurfaces with constant scalar curvature
• Integral formulas for compact space-like hypersurfaces in de Sitter space: Applications to the case of constant higher order mean curvature
• On the volume and the Gauss map image of spacelike hypersurfaces in de Sitter space
• Characterizations of the Sphere by the Curvature of the Second Fundamental Form
• A Characteristic Property of the Sphere
• Two Characteristic Properties of the Sphere
• Closed Convex Hypersurfaces with Second Fundamental Form of Constant Curvature
• Curvature properties of compact spacelike hypersurfaces in de Sitter space

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