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Functional Analysis and Its Applications

, Volume 36, Issue 3, pp 196–204 | Cite as

Compatible Metrics of Constant Riemannian Curvature: Local Geometry, Nonlinear Equations, and Integrability

  • O. I. Mokhov
Article

Abstract

The description problem is solved for compatible metrics of constant Riemannian curvature. Nonlinear equations describing all nonsingular pencils of compatible metrics of constant Riemannian curvature are derived and their integrability by the inverse scattering method is proved. In particular, a Lax pair with a spectral parameter is found for these nonlinear equations. We prove that all nonsingular pairs of compatible metrics of constant Riemannian curvature are described by special integrable reductions of the nonlinear equations defining orthogonal curvilinear coordinate systems in spaces of constant curvature.

flat pencil of metrics, compatible metrics, metric of constant Riemannian curvature, nonlinear integrable equation, Lax pair, compatible Poisson brackets 

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Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • O. I. Mokhov

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