Degenerate Backlund transformation

  • V. A. Gor'kavyi
  • E. N. Nevmerzhitskaya Физ.-техн. ин-т низких температур НАН Украины, Харьков


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.
How to Cite
Gor’kavyi, V. A., and E. N. Nevmerzhitskaya. “Degenerate Backlund Transformation”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, no. 1, Jan. 2016, pp. 38-51,
Research articles