Compatible flat metrics
Differential Geometry
2010-01-04 v1 Mathematical Physics
math.MP
Symplectic Geometry
Exactly Solvable and Integrable Systems
Abstract
We solve the problem of description for nonsingular pairs of compatible flat metrics in the general N-component case. The integrable nonlinear partial differential equations describing all nonsingular pairs of compatible flat metrics (or, in other words, nonsingular flat pencils of metrics) are found and integrated. The integrating of these equations is based on reducing to a special nonlinear differential reduction of the Lame equations and using the Zakharov method of differential reductions in the dressing method (a version of the inverse scattering method).
Cite
@article{arxiv.math/0201224,
title = {Compatible flat metrics},
author = {O. I. Mokhov},
journal= {arXiv preprint arXiv:math/0201224},
year = {2010}
}
Comments
30 pages