On different notions of homogeneity for CR-manifolds. (English) Zbl 1138.32018

Zaitsev, Dmitri

Asian J. Math. 11, No. 2, 331-340 (2007).

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.

Reviewer: Mauro Nacinovich (Roma)

MSC:

32V05	CR structures, CR operators, and generalizations
22E05	Local Lie groups
32V99	CR manifolds

Keywords:

CR-manifold; homogeneity; equivalence; definable; semianalytic