Submanifolds of constant sectional curvature in pseudo-Riemannian manifolds

DOI10.1007/BF00129898zbMath0866.53049OpenAlexW1967583471WikidataQ115395223 ScholiaQ115395223MaRDI QIDQ1126453

Walterson Ferreira, Keti Tenenblat, João Lucas Marques Barbosa

Publication date: 20 July 1997

Published in: Annals of Global Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00129898

zbMATH Keywords

Riemannian manifoldisometric immersionconstant sectional curvatureintrinsic generalized equations

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global submanifolds (53C40) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Local submanifolds (53B25) Local Riemannian geometry (53B20) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72)

Related Items (8)

Bäcklund's theorem for \(n\)-dimensional Lorentzian submanifold in the Minkowski space \(\mathbb E_1^{2n-1}\) ⋮ Curved flats, pluriharmonic maps and constant curvature immersions into pseudo-Riemannian space forms ⋮ Superposition formulae for the geometric Bäcklund transformations of the hyperbolic and elliptic sine-Gordon and sinh-Gordon equations ⋮ Recursion operator for the intrinsic generalized sine-Gordon equation ⋮ Isometric immersions of pseudo-Riemannian space forms ⋮ Reduction of the \(n\)-dimensional static vacuum Einstein equation and generalized Schwarzschild solutions ⋮ Ribaucour transformations for isometric immersions of pseudo-Riemannian space forms ⋮ Twisted hierarchies associated with the generalized sine-Gordon equation

Cites Work

• A higher dimension generalization of the Sine-Gordon equation and its soliton theory
• Bäcklund's theorem for \(n\)-dimensional submanifolds of \(R^{2n-1}\)
• Submanifolds of constant positive curvature. I
• Bäcklund transformations for a class of systems of differential equations
• The low-dimensional metric foliations of Euclidean spheres
• On the symmetry groups of the intrinsic generalized wave and sine–Gordon equations
• Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory
• Pseudospherical Surfaces and Evolution Equations
• Bäcklund's theorem for submanifolds of space forms and a generalized wave equation
• Inverse Scattering and the Bäcklund Transformation for the Generalized Wave and Generalized Sine‐Gordon Equations
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