Reductions of Gauss-Codazzi Equations

DOI10.1111/sapm.12121zbMath1361.35142arXiv1601.04300OpenAlexW3123038040MaRDI QIDQ2953409

Robert Conte, A. Michel Grundland

Publication date: 4 January 2017

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.04300

zbMATH Keywords

integrable systemscurvatureLie symmetriesPainlevé

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Applications of Lie groups to the sciences; explicit representations (22E70)

Related Items (2)

Surfaces de Bonnet et équations de Painlevé ⋮ Group interpretation of the spectral parameter. The case of isothermic surfaces.

Cites Work

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• Bonnet surfaces and isothermic surfaces
• Studies of the Painlevé equations. I: Sixth Painlevé equation \(P_{VI}\)
• Polynomial Hamiltonians associated with Painleve equations. II: Differential equations satisfied by polynomial Hamiltonians
• Surfaces with harmonic inverse mean curvature and Painlevé equations
• Painlevé equations in the differential geometry of surfaces
• Isothermic surfaces in \(\mathbf E^3\) as soliton surfaces
• A characterization of tori with constant mean curvature in space form
• Painlevé Classification of a Class of Differential Equations of the Second Order and Second Degree
• Subalgebras of real three- and four-dimensional Lie algebras
• The Lund–Regge surface and its motion’s evolution equation

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