Different definitions of homogeneity of real hypersurfaces in ℂ2
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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 surfaceM 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 ℂ2.
Key wordshomogeneous hypersurface weakly homogeneous hypersurface Levi nondegenerate real-analytic nonumbilic hypersurfaces in ℂ2 germ of a surface special normal Moser equation local Lie group
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