Geodesic
On the Darboux--Nijenhuis variables on the Poisson manifold~$so^*(4)$
Russian journal of nonlinear dynamics, Tome 3 (2007) no. 2, pp. 141-155.

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We classify quadratic Poisson structures on $so^*(4)$ and $e^*(3)$, which have the same foliations by symplectic leaves as canonical Lie-Poisson tensors. The separated variables for some of the corresponding bi-integrable systems are constructed.
Keywords: integrable system, bi-hamiltonian geometry, separation of variables. 
@article{ND_2007_3_2_a1,
     author = {A. V. Vershilov and A. V. Tsiganov},
     title = {On the {Darboux--Nijenhuis} variables on the {Poisson} manifold~$so^*(4)$},
     journal = {Russian journal of nonlinear dynamics},
     pages = {141--155},
     publisher = {mathdoc},
     volume = {3},
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     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2007_3_2_a1/}
}
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A. V. Vershilov; A. V. Tsiganov. On the Darboux--Nijenhuis variables on the Poisson manifold~$so^*(4)$. Russian journal of nonlinear dynamics, Tome 3 (2007) no. 2, pp. 141-155. http://geodesic.mathdoc.fr/item/ND_2007_3_2_a1/