Finite type submanifolds in pseudo-Euclidean spaces and applications

DOI10.2996/kmj/1138037104zbMath0586.53022OpenAlexW2080276551MaRDI QIDQ1071327

Bang-Yen Chen

Publication date: 1985

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

Full work available at URL: https://doi.org/10.2996/kmj/1138037104

zbMATH Keywords

scalar curvaturemean curvaturespace-like submanifoldpseudo-Euclidean spacesubmanifold of finite type

Mathematics Subject Classification ID

Global submanifolds (53C40) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50)

Related Items (21)

Submanifolds in de Sitter space-time satisfying \(\Delta H = \lambda H\) ⋮ Reductive homogeneous pseudo-Riemannian manifolds ⋮ On Chen surfaces in a Minkowski space time ⋮ Pseudo-spherical submanifolds with 1-type pseudo-spherical Gauss map ⋮ Birotational hypersurface and the second Laplace-Beltrami operator in the four dimensional Euclidean space ${\mathbb{E}}^{4}$ ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Differential Geometry of 1-type Submanifolds and Submanifolds with 1-type Gauss Map ⋮ \(B\)-scrolls with non-diagonalizable shape operators. ⋮ Isotropic submanifolds of pseudo-Riemannian spaces ⋮ Biharmonic hypersurfaces in a sphere ⋮ Biharmonic submanifolds of pseudo-Riemannian manifolds ⋮ Null finite type hypersurfaces in space forms ⋮ On submanifolds with 2-type pseudo-hyperbolic Gauss map in pseudo-hyperbolic space ⋮ On biminimal submanifolds in nonpositively curved manifolds ⋮ Complete explicit classification of parallel Lorentz surfaces in arbitrary pseudo-Euclidean spaces ⋮ Classifications of flat surfaces with generalized 1-type Gauss map in \(\mathbb L^{3}\) ⋮ Hyperbolic submanifolds with finite type hyperbolic Gauss map ⋮ Complete classification of spatial surfaces with parallel mean curvature vector in arbitrary non-flat pseudo-Riemannian space forms ⋮ Correction to: 3-dimensional space-like submanifolds with parallel mean curvature vector of an indefinite space form ⋮ Pseudo-totally umbilical lightlike submanifolds

Cites Work

• Isometric immersions of Lorentz space with parallel second fundamental forms
• The Large Scale Structure of Space-Time
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