Geodesic
Construction of completely integrable geodesic flows on compact symmetric spaces
Izvestiya. Mathematics , Tome 29 (1987) no. 1, pp. 19-31.

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On every compact symmetric space, Riemannian metrics are constructed for which the geodesic flow is completely integrable in the sense of Liouville. Some of the metrics constructed in the case of a sphere are conformally equivalent to metrics on $n$-axial ellipsoids. Bibliography: 22 titles. 
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A. V. Brailov. Construction of completely integrable geodesic flows on compact symmetric spaces. Izvestiya. Mathematics , Tome 29 (1987) no. 1, pp. 19-31. http://geodesic.mathdoc.fr/item/IM2_1987_29_1_a1/

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