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Funktsional'nyi Analiz i ego Prilozheniya, 2002, Volume 36, Issue 3, Pages 36–47
DOI: https://doi.org/10.4213/faa202
(Mi faa202)
 

This article is cited in 10 scientific papers (total in 10 papers)

Compatible Metrics of Constant Riemannian Curvature: Local Geometry, Nonlinear Equations, and Integrability

O. I. Mokhov

Landau Institute for Theoretical Physics, Centre for Non-linear Studies
References:
Abstract: The description problem is solved for compatible metrics of constant Riemannian curvature. Nonlinear equations describing all nonsingular pencils of compatible metrics of constant Riemannian curvature are derived and their integrability by the inverse scattering method is proved. In particular, a Lax pair with a spectral parameter is found for these nonlinear equations. We prove that all nonsingular pairs of compatible metrics of constant Riemannian curvature are described by special integrable reductions of the nonlinear equations defining orthogonal curvilinear coordinate systems in spaces of constant curvature.
Keywords: flat pencil of metrics, compatible metrics, metric of constant Riemannian curvature, nonlinear integrable equation, Lax pair, compatible Poisson brackets.
Received: 24.12.2001
English version:
Functional Analysis and Its Applications, 2002, Volume 36, Issue 3, Pages 196–204
DOI: https://doi.org/10.1023/A:1020145920947
Bibliographic databases:
Document Type: Article
UDC: 517.986+512.54
Language: Russian
Citation: O. I. Mokhov, “Compatible Metrics of Constant Riemannian Curvature: Local Geometry, Nonlinear Equations, and Integrability”, Funktsional. Anal. i Prilozhen., 36:3 (2002), 36–47; Funct. Anal. Appl., 36:3 (2002), 196–204
Citation in format AMSBIB
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  • https://doi.org/10.4213/faa202
  • https://www.mathnet.ru/eng/faa/v36/i3/p36
  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Функциональный анализ и его приложения Functional Analysis and Its Applications
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