@article{Gor’kavyi_Nevmerzhitskaya_2016, title={Degenerate Backlund transformation}, volume={68}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/1820}, abstractNote={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.}, number={1}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Gor’kavyi, V. A. and Nevmerzhitskaya, E. N.}, year={2016}, month={Jan.}, pages={38-51} }