Complete maximal spacelike submanifolds

DOI10.2996/KMJ/1138043791zbMath0908.53033OpenAlexW2046577400MaRDI QIDQ1392772

Susumu Ishikawa, Qing-Ming Cheng

Publication date: 18 October 1998

Published in: Kodai Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2996/kmj/1138043791

zbMATH Keywords

scalar curvatureRicci curvaturesectional curvaturetotally geodesic submanifoldSimon's methodspacelike maximal submanifold

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)

Related Items (7)

Willmore spacelike submanifolds in an indefinite space form Nn+p q(c) ⋮ Linear Weingarten spacelike submanifolds in semi-Riemannian space form ⋮ Stochastically complete, parabolic and \(L^1\)-Liouville spacelike submanifolds with parallel mean curvature vector ⋮ A characterization of linear Weingarten submanifolds in a semi-Riemannian space form with arbitrary index ⋮ Spacelike submanifolds with parallel mean curvature vector in \(S_{q}^{n+p}(1)\) ⋮ Spacelike submanifolds in the de Sitter space \(S_p^{n+p}(c)\) with constant scalar curvature ⋮ Spacelike submanifolds with parallel mean curvature vector in a de Sitter space \(S^{n+p}_q(c)\)

Cites Work

• An intrinsic rigidity theorem for minimal submanifolds in a sphere
• Maximal spacelike submanifolds of a pseudo-Riemannian space of constant curvature
• Integral formulas for compact spacelike \(n\)-submanifolds in de Sitter spaces. Applications to the parallel mean curvature vector case
• Minimal varieties in Riemannian manifolds
• Submanifolds with Constant Mean Curvature
• Minimal Submanifolds of a Sphere with Second Fundamental Form of Constant Length

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