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Uspekhi Mat. Nauk, 2017, Volume 72, Issue 5(437), Pages 113–164 (Mi umn9792)  

This article is cited in 1 scientific paper (total in 1 paper)

Pencils of compatible metrics and integrable systems

O. I. Mokhov

Lomonosov Moscow State University

Abstract: This survey is devoted to the theory of pencils of compatible Riemannian and pseudo-Riemannian metrics, related non-linear integrable systems, and applications.
Bibliography: 82 titles.

Keywords: compatible metrics, compatible connections and curvatures, orthogonal curvilinear coordinate systems, Nijenhuis tensor, Riemann invariants, integrable systems, systems of hydrodynamic type.

Funding Agency Grant Number
Russian Science Foundation 16-11-10260
This work was supported by the Russian Science Foundation under grant 16-11-10260.


DOI: https://doi.org/10.4213/rm9792

Full text: PDF file (898 kB)
First page: PDF file
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English version:
Russian Mathematical Surveys, 2017, 72:5, 889–937

Bibliographic databases:

MSC: Primary 37K10, 37K25, 53B21, 53C21; Secondary 53B50
Received: 21.06.2017

Citation: O. I. Mokhov, “Pencils of compatible metrics and integrable systems”, Uspekhi Mat. Nauk, 72:5(437) (2017), 113–164; Russian Math. Surveys, 72:5 (2017), 889–937

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/umn/v72/i5/p113

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. V. Glukhov, O. I. Mokhov, “On algebraic-geometry methods for constructing flat diagonal metrics of a special form”, Russian Math. Surveys, 74:4 (2019), 761–763  mathnet  crossref  crossref  adsnasa  isi  elib
  • Успехи математических наук Russian Mathematical Surveys
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