Geodesic
Affine surfaces which are quasihomogeneous with respect to an algebraic group
Izvestiya. Mathematics , Tome 5 (1971) no. 4, pp. 754-769.

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In this paper we give a classification of affine surfaces which are quasihomogeneous with respect to an algebraic group. In particular, we also obtain a classification of affine surfaces which are homogeneous with respect to an algebraic group. 
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M. Kh. Gizatullin. Affine surfaces which are quasihomogeneous with respect to an algebraic group. Izvestiya. Mathematics , Tome 5 (1971) no. 4, pp. 754-769. http://geodesic.mathdoc.fr/item/IM2_1971_5_4_a1/

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