An analog of Bianchi transformations for two-dimensional surfaces in the space \(S^{3} \times \mathbb R^{1}\)

DOI10.1134/S000143461105021XzbMath1252.53069MaRDI QIDQ650502

E. N. Nevmerzhitskaya, Vasyl A. Gorkavyy

Publication date: 25 November 2011

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

zbMATH Keywords

Bäcklund transformationGaussian curvature2-surface negative intrinsic curvatureBianchi transformationpseudospherical congruencepseudospherical surface

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Cites Work

• Bäcklund's theorem for \(n\)-dimensional submanifolds of \(R^{2n-1}\)
• On Bianchi and Bäcklund transformations of two-dimensional surfaces in \(E^4\)
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