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

A. V. Bolsinov   ; V. S. Matveev   ; A. T. Fomenko

Sbornik. Mathematics, Tome 189 (1998) no. 10, pp. 1441-1466

Résumé

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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