Degenerate Backlund transformation

• Дата: 2016
• Автори: Gor'kavyi, V. A., Nevmerzhitskaya, E. N., Горькавий, В. А., Невмержицкая, Е. Н.
• Формат: Стаття
• Мова: Російська
• Опубліковано: Institute of Mathematics, NAS of Ukraine 2016
• Онлайн доступ: https://umj.imath.kiev.ua/index.php/umj/article/view/1820
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

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 consta...