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We show that various notions of local homogeneity for CR-manifolds are equivalent. In particular, if germs at any two points of a CR-manifold are CR-equivalent, there exists a transitive local Lie group action by CR-automorphisms near every point.

Keywords

CR-manifold, homogeneity, equivalence, definable, semianalytic

2010 Mathematics Subject Classification

22E05, 32V05, 32Vxx

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Published 1 January 2007