Compatible flat metrics
微分几何
2010-01-04 v1 数学物理
math.MP
辛几何
可精确求解与可积系统
摘要
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).
引用
@article{arxiv.math/0201224,
title = {Compatible flat metrics},
author = {O. I. Mokhov},
journal= {arXiv preprint arXiv:math/0201224},
year = {2010}
}
备注
30 pages