Reductions of Gauss–Codazzi Equations. Issue 3 (8th March 2016)

• Record Type: Journal Article
• Authors: Conte, Robert; Grundland, A. Michel
• Is Part Of: Studies in applied mathematics. Volume 137:Issue 3(2016)
• Page Start: 306
• Page End: 327
• Publication Date: 2016-03-08
• Subjects: Mathematics -- Periodicals; Mathématiques -- Périodiques; Mathématique; Mathématique appliquée; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); 519
• DOI: 10.1111/sapm.12121
• Languages: English
• ISSNs: 0022-2526

Abstract

Abstract : We prove that conformally parameterized surfaces in Euclidean space R 3 ( c ) of curvature c admit a symmetry reduction of their Gauss–Codazzi equations whose general solution is expressed with the sixth Painlevé function. Moreover, it is shown that the two known solutions of this type (Bonnet 1867, Bobenko et al. 1997) can be recovered by such a reduction.