Compatible metrics of constant Riemannian curvature: local geometry, nonlinear equations, and integrability

DOI10.1023/A:1020145920947zbMath1083.53041arXivmath/0201280MaRDI QIDQ1812433

Oleg I. Mokhov

Publication date: 2002

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0201280

zbMATH Keywords

Lamé equationsDarboux equation\(n\)-wave equationscompatible bracketscompatible nonlocal Poisson brackets of hydrodynamic typeDubrovin-Novikovequation of axisymmetric vibrations of a gasMokhov-Ferapontovspecial integrable reductions of the nonlinear equations for nonsingular pencils of constant curvaturetriple of pairwise commuting Monge-Ampère equationsZakharov Method of differential reductions

Mathematics Subject Classification ID

Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Global Riemannian geometry, including pinching (53C20) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Local Riemannian geometry (53B20)

Related Items (5)

Compatible metrics and the diagonalizability of nonlocally bi-Hamiltonian systems of hydrodynamic type ⋮ Pencils of compatible metrics and integrable systems ⋮ On metrics of diagonal curvature ⋮ On orthogonal curvilinear coordinate systems in constant curvature spaces ⋮ Orthogonal curvilinear coordinate systems corresponding to singular spectral curves

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