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

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

2002-01-29

arxiv.org/abs/math/0201280v1

Functional Analysis and its Applications, Vol. 36, No. 3, 2002, 196-204.

Mathematics

Differential Geometry

12 pages

Scientific paper

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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