Geodesic
On affine surfaces that can be completed by a nonsingular rational
Izvestiya. Mathematics, Tome 4 (1970) no. 4, pp. 787-810 
M. Kh. Gizatullin. On affine surfaces that can be completed by a nonsingular rational. Izvestiya. Mathematics, Tome 4 (1970) no. 4, pp. 787-810. http://geodesic.mathdoc.fr/item/IM2_1970_4_4_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that an affine nonsingular surface which can be completed by a nonsingular rational curve is quasi-homogeneous. The homogeneity of such surfaces is proved in the case of characteristic zero.

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