On some integrable cases in surface theory

DOI10.1007/BF02364876zbMath0964.53007MaRDI QIDQ1303376

Dmitry Korotkin

Publication date: 5 October 1999

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/68764

zbMATH Keywords

theta functionGaussian curvaturesoliton surfaceBianchi surfacecoupled Ernst system

Mathematics Subject Classification ID

Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Surfaces in Euclidean and related spaces (53A05) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Related Items (6)

Surfaces in \(\mathbb{R}^ 3\) with prescribed curvature ⋮ Isomonodromic quantization of dimensionally reduced gravity ⋮ On the differential-difference sine-Gordon equation with an integral type source ⋮ Some remarks on finite-gap solutions of the Ernst equation. ⋮ Deformations of surfaces associated with integrable Gauss–Mainardi–Codazzi equations ⋮ Computational approach to hyperelliptic Riemann surfaces

Cites Work

• Liouville's theorem and the method of the inverse problem
• Bianchi surfaces in \(\mathbb{R}^ 3\) and deformation of hyperelliptic curves
• Tata lectures on theta. I: Introduction and motivation: Theta functions in one variable. Basic results on theta functions in several variables. With the assistance of C. Musili, M. Nori, E. Previato, and M. Stillman
• Theta functions on Riemann surfaces
• Elliptic solutions of stationary axisymmetric Einstein equations
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