Geodesic
Commutative homogeneous spaces with one-dimensional stabilizer
Izvestiya. Mathematics , Tome 76 (2012) no. 4, pp. 820-839.

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We find all homogeneous spaces $X=G/H$ of algebraic groups with one-dimensional stabilizer for which the action $G :T^*X$ is co-isotropic (that is, the tangent space of a generic $G$-orbit is co-isotropic).
Keywords: commutative homogeneous space, action of algebraic groups. 
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S. A. Shashkov. Commutative homogeneous spaces with one-dimensional stabilizer. Izvestiya. Mathematics , Tome 76 (2012) no. 4, pp. 820-839. http://geodesic.mathdoc.fr/item/IM2_2012_76_4_a6/

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