Compatible metrics of constant Riemannian curvature: local geometry, nonlinear equations and integrability
Mokhov, O. I.
Differential Geometry
Mathematical Physics
Symplectic Geometry
Exactly Solvable and Integrable Systems
Original · EN
The nonlinear equations describing all the nonsingular pencils of metrics of constant Riemannian curvature are derived and the integrability of these nonlinear equations by the method of inverse scattering problem is proved. It is proved that all the nonsingular pairs of compatible metrics of constant Riemannian curvature are described by special integrable reductions of nonlinear equations defining orthogonal curvilinear coordinate systems in the spaces of constant curvature.
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