Painlevé equations in the differential geometry of surfaces

DOI10.1007/b76883zbMath0970.53002OpenAlexW1967208361MaRDI QIDQ1589918

Ulrich Eitner, Alexander Ivanovich Bobenko

Publication date: 19 December 2000

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

Full work available at URL: http://link.springer.de/link/service/series/0304/tocs/t1753.htm

zbMATH Keywords

Painlevé property constant mean curvature constant negative curvature spectral parameter isomonodromic deformation affine differential geometry soliton theory affine sphere Bonnet surface Amsler surface Smyth surfaces Zakharov-Shabad representation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Surfaces in Euclidean and related spaces (53A05) Research exposition (monographs, survey articles) pertaining to differential geometry (53-02) Affine differential geometry (53A15) Research exposition (monographs, survey articles) pertaining to ordinary differential equations (34-02)

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