## Journal of Applied Mathematics

### Compatible flat metrics

Oleg I. Mokhov

#### Abstract

We solve the problem of description of nonsingular pairs of compatible flat metrics for 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 Lamé equations and using the Zakharov method of differential reductions in the dressing method (a version of the inverse scattering method).

#### Article information

Source
J. Appl. Math., Volume 2, Number 7 (2002), 337-370.

Dates
First available in Project Euclid: 30 March 2003

https://projecteuclid.org/euclid.jam/1049074868

Digital Object Identifier
doi:10.1155/S1110757X02203149

Mathematical Reviews number (MathSciNet)
MR1942027

Zentralblatt MATH identifier
1008.37041

#### Citation

Mokhov, Oleg I. Compatible flat metrics. J. Appl. Math. 2 (2002), no. 7, 337--370. doi:10.1155/S1110757X02203149. https://projecteuclid.org/euclid.jam/1049074868

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