The Bäcklund transforms of Peterson’s isometric deformations of paraboloids

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• 作者：Ion I. Dincă
• 关键词：Bäcklund transformation ; Bianchi Permutability Theorem ; Common conjugate systems ; (Peterson’s)  deformations of quadrics
• 刊名：Rendiconti del Circolo Matematico di Palermo
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：65
• 期：3
• 页码：473-484
• 全文大小：427 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Algebra
  Geometry
  Analysis
  Applications of Mathematics
  
• 出版者：Springer Milan
• ISSN：1973-4409
• 卷排序：65

文摘

In trying to provide explicit isometric deformations of quadrics our investigation is to use Bianchi’s link between real or imaginary isometric deformations of totally real regions of real paraboloids and various totally real forms of the sine-Gordon equation coupled with Bianchi’s simple observation that the vacuum soliton of these totally real forms of the sine-Gordon equation provides precisely Peterson’s isometric deformations of such paraboloids in order to derive explicit Bäcklund transforms of Peterson’s isometric deformations of paraboloids.