2017
Том 69
№ 9

All Issues

Degenerate Backlund transformation

Gor'kavyi V. A., Nevmerzhitskaya E. N.


Abstract

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.

Citation Example: Gor'kavyi V. A., Nevmerzhitskaya E. N. Degenerate Backlund transformation // Ukr. Mat. Zh. - 2016. - 68, № 1. - pp. 38-51.