The topology of Riemannian manifolds with integrable geodesics flows
Trudy Matematicheskogo Instituta imeni V.A. Steklova, New results in the theory of topological classification of integrable systems, Tome 205 (1994), pp. 150-163.

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@article{TM_1994_205_a12,
     author = {I. A. Taimanov},
     title = {The topology of {Riemannian} manifolds with integrable geodesics flows},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {150--163},
     publisher = {mathdoc},
     volume = {205},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_1994_205_a12/}
}
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I. A. Taimanov. The topology of Riemannian manifolds with integrable geodesics flows. Trudy Matematicheskogo Instituta imeni V.A. Steklova, New results in the theory of topological classification of integrable systems, Tome 205 (1994), pp. 150-163. http://geodesic.mathdoc.fr/item/TM_1994_205_a12/