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On different notions of homogeneity for CR-manifolds. (English) Zbl 1138.32018
The Author shows the equivalence of different notions of local homogeneity for CR manifolds. He generalizes the results of A. V. Loboda [Math. Notes 64, No. 6, 761–766 (1998); translation from Mat. Zametki 64, No. 6, 881–887 (1998; Zbl 0949.32019)] for hypersurfaces in $$\mathbb{C}^2$$ to the case of real-analytic CR manifolds of arbitrary CR dimension and CR codimension. The investigation relies on results of jet parametrization (see M. S. Baouendi, L. P. Rothschild and D. Zaitsev [J. Differ. Geom. 59, No. 2, 301–351 (2001; Zbl 1037.32030)]) and on general properties of semianalytic sets.

##### MSC:
 32V05 CR structures, CR operators, and generalizations 22E05 Local Lie groups 32V99 CR manifolds
##### Keywords:
CR-manifold; homogeneity; equivalence; definable; semianalytic
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