Bonnet surfaces and Painlevé equations
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Publication:4398648
DOI10.1515/crll.1998.061zbMath0906.53001OpenAlexW1997089009MaRDI QIDQ4398648
Ulrich Eitner, Alexander Ivanovich Bobenko
Publication date: 20 July 1998
Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)
Full work available at URL: http://cds.cern.ch/record/277190
Painlevé equationEuclidean 3-spaceLax representationBonnet surfacesdeformations preserving principal curvatures
Explicit solutions, first integrals of ordinary differential equations (34A05) Other functions coming from differential, difference and integral equations (33E30) Surfaces in Euclidean and related spaces (53A05)
Related Items (13)
On the problem of isometry of a hypersurface preserving mean curvature ⋮ Bonnet and isotropically isothermic surfaces in 4-dimensional space forms ⋮ Bonnet surfaces with constant curvature ⋮ Over-determined systems in relation to principal curvatures ⋮ Generalized Bonnet surfaces and Lax pairs of PVI ⋮ Timelike Bonnet surfaces in Lorentzian space forms. ⋮ Compact surfaces with no Bonnet mate ⋮ Bonnet pairs and isothermic surfaces ⋮ On surfaces with prescribed shape operator ⋮ The Painlevé III, V and VI transcendents as solutions of the Einstein-Weyl equations ⋮ Tangential developable surfaces as Bonnet surfaces ⋮ Bonnet ruled surfaces ⋮ Bour's theorem and helicoidal surfaces with constant mean curvature in the Bianchi-Cartan-Vranceanu spaces
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