Compatible metrics of constant Riemannian curvature: local geometry, nonlinear equations and integrability
Differential Geometry
2010-01-04 v1 Mathematical Physics
math.MP
Symplectic Geometry
Exactly Solvable and Integrable Systems
Abstract
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.
Keywords
Cite
@article{arxiv.math/0201280,
title = {Compatible metrics of constant Riemannian curvature: local geometry, nonlinear equations and integrability},
author = {O. I. Mokhov},
journal= {arXiv preprint arXiv:math/0201280},
year = {2010}
}
Comments
12 pages