Degenerate Backlund transformation - Gor'kavyi, V. A.; Nevmerzhitskaya, E. N. (Ukrains’kyi Matematychnyi Zhurnal, 2016)
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 ≥ 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 ≥ 4 that admit degenerate Bianchi transformations is obtained. Moreover, we also obtain a complete classification of pseudospherical surfaces in R^n, n ≥ 4, admitting degenerate Backlund transformations into straight lines.