2019
Том 71
№ 6

# Degenerate Backlund transformation

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.

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