Gor'kavyi V. A.
Ukr. Mat. Zh. - 2016. - 68, № 1. - pp. 38-51
A concept of degenerate B¨acklund transformation is introduced for two-dimensional surfaces in many-dimensional Euclidean spaces. It is shown that if a surface in $R^n, n \geq 4$, admits a degenerate B¨acklund transformation, then this surface is pseudospherical, i.e., its Gauss curvature is constant and negative. The complete classification of pseudospherical surfaces in $R^n, n \geq 4$ that admit degenerate Bianchi transformations is obtained. Moreover, we also obtain a complete classification of pseudospherical surfaces in $R^n, n \geq 4$, admitting degenerate Backlund transformations into straight lines.
Ukr. Mat. Zh. - 2011. - 63, № 11. - pp. 1460-1468
We classify two-dimensional pseudospherical surfaces with degenerate Bianchi transformation in a multidimensional Euclidean space.