Generalization of the Bianchi-Bäcklund transformation of pseudo-spherical surfaces

DOI10.1007/s10958-015-2380-yzbMath1320.53061OpenAlexW1980995834MaRDI QIDQ2515235

Vasyl A. Gorkavyy

Publication date: 31 July 2015

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-015-2380-y

zbMATH Keywords

space of constant curvatureBianchi transformationpseudo-spherical Bianchi congruencepseudo-spherical submanifolds

Mathematics Subject Classification ID

Global submanifolds (53C40) Surfaces in Euclidean and related spaces (53A05) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Related Items

Circular Dini surfaces in \(\mathbb{E}^4\) ⋮ Degenerate Bianchi transformations for three-dimensional pseudo-spherical submanifolds in \(\mathbb{R}^5\)

Cites Work

• A higher dimension generalization of the Sine-Gordon equation and its soliton theory
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• On Bianchi and Bäcklund transformations of two-dimensional surfaces in \(E^4\)
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• Two-dimensional pseudospherical surfaces with degenerate Bianchi transformation
• Isometric imbedding of Riemann manifolds in a Riemann manifold
• Grassmann manifolds and the Grassmann image of submanifolds
• A higher dimension generalization of the Sine-Gordon equation and its Bäcklund transformation
• Bäcklund's theorem for submanifolds of space forms and a generalized wave equation
• Bianchi congruences of two-dimensional surfaces in $ E^4$
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