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Mat. Sb., 1998, Volume 189, Number 10, Pages 5–32 (Mi msb346)  

This article is cited in 40 scientific papers (total in 40 papers)

Two-dimensional Riemannian metrics with integrable geodesic flows. Local and global geometry

A. V. Bolsinova, V. S. Matveeva, A. T. Fomenko

a M. V. Lomonosov Moscow State University

Abstract: Classical and new results on integrable geodesic flows on two-dimensional surfaces are reviewed. The central question is the classification of such flows up to various equivalences, of which the following four kinds are the most interesting ones: 1) isometry; 2) geodesic equivalence; 3) orbital equivalence; 4) Liouville equivalence.


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English version:
Sbornik: Mathematics, 1998, 189:10, 1441–1466

Bibliographic databases:

UDC: 513.83
MSC: Primary 58F17, 58F07; Secondary 58F05
Received: 04.06.1998

Citation: A. V. Bolsinov, V. S. Matveev, A. T. Fomenko, “Two-dimensional Riemannian metrics with integrable geodesic flows. Local and global geometry”, Mat. Sb., 189:10 (1998), 5–32; Sb. Math., 189:10 (1998), 1441–1466

Citation in format AMSBIB
\by A.~V.~Bolsinov, V.~S.~Matveev, A.~T.~Fomenko
\paper Two-dimensional Riemannian metrics with integrable geodesic flows. Local and global geometry
\jour Mat. Sb.
\yr 1998
\vol 189
\issue 10
\pages 5--32
\jour Sb. Math.
\yr 1998
\vol 189
\issue 10
\pages 1441--1466

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    7. Dullin H.R., Matveev V.S., “A new natural Hamiltonian system on T*S-2 admitting an integral of degree 3 in momenta”, Global Analysis and Applied Mathematics, Aip Conference Proceedings, 729, 2004, 141–146  crossref  mathscinet  zmath  adsnasa  isi
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