Geodesic
The symplectic leaves on Poisson homogeneous spaces of Poisson--Lie groups
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 2 (1995), pp. 306-311.

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The symplectic leaves on Poisson homogeneous spaces of a Poisson–Lie group $G$ are described in terms of the double $D(G)$. An explicit formula for the symplectic form on a leaf is derived. A duality between the symplectic leaves on the Poisson homogeneous spaces of $G$ and those of the dual group $G^*$ is revealed. 
@article{JMAG_1995_2_a3,
     author = {E. A. Karolinsky},
     title = {The symplectic leaves on {Poisson} homogeneous spaces of {Poisson--Lie} groups},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {306--311},
     publisher = {mathdoc},
     volume = {2},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JMAG_1995_2_a3/}
}
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E. A. Karolinsky. The symplectic leaves on Poisson homogeneous spaces of Poisson--Lie groups. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 2 (1995), pp. 306-311. http://geodesic.mathdoc.fr/item/JMAG_1995_2_a3/