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

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©, 1998 Russian Academy of Sciences, (DoM) and London Mathematical Society, Turpion Ltd
, , Citation A V Bolsinov et al 1998 Sb. Math. 189 1441 DOI 10.1070/SM1998v189n10ABEH000346

1064-5616/189/10/1441

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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10.1070/SM1998v189n10ABEH000346