Mathematical Notes

, Volume 64, Issue 6, pp 761–766 | Cite as

Different definitions of homogeneity of real hypersurfaces in ℂ2

  • A. V. Loboda


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 words

homogeneous 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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Copyright information

© Kluwer Academic/Plenum Publishers 1999

Authors and Affiliations

  • A. V. Loboda
    • 1
  1. 1.Voronezh State Architectural and Building AcademyUSSR

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