On Bianchi and Bäcklund transformations of two-dimensional surfaces in \(E^4\). (English) Zbl 0983.53006
Authors’ abstract: In this paper we discuss the existence and properties of the Bianchi transformations for pseudospherical surfaces in \(E^4\). The results of the paper show that the theory of Bianchi transformations in the discussed case is essentially different from the well-known case of pseudospherical surfaces in \(E^3\) (in general \(n\)-manifolds of constant and negative curvature in \(E^{2n-1})\).
Reviewer: V.Cruceanu (Iaşi)
MSC:
53A07 | Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces |
37K35 | Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems |
53A25 | Differential line geometry |