Geodesic
Different definitions of homogeneity of real hypersurfaces in $\mathbb C^2$
Matematičeskie zametki, Tome 64 (1998) no. 6, pp. 881-887.

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The coincidence of two definitions of local homogeneity for real-analytic hypersurfaces in two-dimensional complex spaces is proved. It is shown that if any two germs of a Levi nondegenerate nonspherical surface $M$ are equivalent, then this surface has a local Lie group structure: $M$ then acts transitively on itself by left shifts, and each such shift is a local holomorphic transformation of $\mathbb C^2$. 
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A. V. Loboda. Different definitions of homogeneity of real hypersurfaces in $\mathbb C^2$. Matematičeskie zametki, Tome 64 (1998) no. 6, pp. 881-887. http://geodesic.mathdoc.fr/item/MZM_1998_64_6_a8/

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