Geodesic
Integrability of the Euler equations on homogeneous symplectic manifolds
Sbornik. Mathematics, Tome 34 (1978) no. 6, pp. 707-713

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Any strictly homogeneous symplectic manifold $M$ with a group of motions $\mathscr G$ may be considered as an orbit of the coadjoint action of $\mathscr G$. Therefore all Hamiltonian systems defined on an orbit, in particular Euler's equations, are carried over to $M$ in a natural way. In this paper a multiparameter family of systems of Euler equations is constructed on $M$, and their complete integrability (in the Liouville sense) is proved. Bibliography: 6 titles. 
@article{SM_1978_34_6_a1,
     author = {D\`ao Trong Thi},
     title = {Integrability of the {Euler} equations on homogeneous symplectic manifolds},
     journal = {Sbornik. Mathematics},
     pages = {707--713},
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     volume = {34},
     number = {6},
     year = {1978},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1978_34_6_a1/}
}
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Dào Trong Thi. Integrability of the Euler equations on homogeneous symplectic manifolds. Sbornik. Mathematics, Tome 34 (1978) no. 6, pp. 707-713. http://geodesic.mathdoc.fr/item/SM_1978_34_6_a1/