TY - JOUR
AU - V. A. Gor'kavyi
AU - E. N. Nevmerzhitskaya
PY - 2016/01/25
Y2 - 2024/02/27
TI - Degenerate Backlund transformation
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 68
IS - 1
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/1820
AB - 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.
ER -