Compatible flat metrics

Details Compatible flat metrics Compatible flat metrics

2002-01-23

arxiv.org/abs/math/0201224v1

Journal of Applied Math.,Vol. 2, No. 7, 2002, 337-370

Mathematics

Differential Geometry

30 pages

Scientific paper

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).

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