Orthogonal curvilinear coordinate systems corresponding to singular spectral curves

DOI10.1134/S0081543806040146zbMath1351.37255arXivmath/0601062OpenAlexW2017565171MaRDI QIDQ2342266

Andrey E. Mironov, Iskander A. Taimanov

Publication date: 11 May 2015

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0601062

Mathematics Subject Classification ID

Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Relationships between algebraic curves and integrable systems (14H70) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20)

Related Items (9)

On an algebro-geometric approach to Ribaucour transformations and Bianchi cubes ⋮ On algebraic-geometric methods for constructing submanifolds with flat normal bundle and holonomic net of curvature lines ⋮ Pencils of compatible metrics and integrable systems ⋮ Orthogonal curvilinear coordinate systems and torsion-free sheaves over reducible spectral curves ⋮ Algebraic-geometry approach to construction of semi-Hamiltonian systems of hydrodynamic type ⋮ On metrics of diagonal curvature ⋮ On orthogonal curvilinear coordinate systems in constant curvature spaces ⋮ Minimal Lagrangian submanifolds in \(\mathbb{CP}^n\) with diagonal metric ⋮ On algebraic-geometry methods for constructing flat diagonal metrics of a special form

Cites Work

• Algebraic-geometric \(n\)-orthogonal curvilinear coordinate systems and solutions of the associativity equations
• Compatible metrics of constant Riemannian curvature: local geometry, nonlinear equations, and integrability
• Description of the \(n\)-orthogonal curvilinear coordinate systems and Hamiltonian integrable systems of hydrodynamic type. I: Integration of the Lamé equations
• Hitchin system on singular curves
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