Related papers: On different notions of homogeneity for CR-manifol…
We consider locally homogeneous $CR$ manifolds and show that, under a condition only depending on their underlying contact structure, their $CR$ automorphisms form a finite dimensional Lie group.
We classify all compact simply connected homogeneous CR manifolds $M$ of codimension one and with non-degenerate Levi form up to CR equivalence. The classification is based on our previous results and on a description of the maximal…
Germs of locally homogeneous CR manifolds M can be characterized in terms of certain algebraic data, e.g., by CR-algebras. We give an explicit formula which relates the Levi form of such an M and its higher order analogues to the Lie…
In this paper we show some results on homogeneous CR manifolds, proved by introducing their associated CR algebras. In particular, we give different notions of nondegeneracy (generalizing the usual notion for the Levi form) which correspond…
Locally homogeneous CR-manifolds in dimension 3 were classified, up to local CR-equivalence, by E.Cartan. We classify, up to local CR-equivalence, all locally homogeneous CR-manifolds in dimension 4. The classification theorem enables us…
Corollary: Two germs of minimal real analytic CR-generic manifolds are formally equivalent if and only if they are biholomorphic.
Given any real-analytic CR manifold M, we provide general conditions on M guaranteeing that the group of all its global real-analytic CR automorphisms is a Lie group (in an appropriate topology). Our conditions are in particular satisfied…
In this article, we solve the equivalence problem for 2--nondegenerate CR geometries that have (at every point) a homogeneous space $G/H$ as a maximally symmetric model for $G$ simple real Lie group of CR automorphisms. This completes the…
A method is proposed to obtain examples of smooth CR-manifolds whose local stability group is neither a Lie group nor infinite-dimensional.
Every open and orientable three manifold has a CR structure which is locally equivalent to the standard CR structure on $S^3$.
We consider canonical fibrations and algebraic geometric structures on homogeneous CR manifolds, in connection with the notion of CR algebra. We give applications to the classifications of left invariant CR structures on semisimple Lie…
In this paper we shall give sufficient conditions for local CR diffeomorphisms between two real analytic submanifolds of $\Bbb C^N$ to be determined by finitely many derivatives at finitely many points. These conditions will also be shown…
Let M be a connected generic real-analytic CR-submanifold of a finite-dimensional complex vector space E. Suppose that for every point a in M the Lie algebra hol(M,a) of germs of all infinitesimal real-analytic CR-automorphisms of M at a is…
We classify the normal CR structures on $S^3$ and their automorphism groups. Together with [3], this closes the classification of normal CR structures on contact 3-manifolds. We give a criterion to compare 2 normal CR structures, and we…
Let M be a compact manifold, possibly with boundary. We show that the group of homeomorphisms of M has the automatic continuity property: any homomorphism from Homeo(M) to any separable group is necessarily continuous. This answers a…
We consider a class of stratified groups with a CR structure and a compatible control distance. For these Lie groups we show that the space of conformal maps coincide with the space of CR and anti-CR diffeomorphisms. Furthermore, we prove…
We investigate CR-manifolds which are tubes M:= F x iV over general bases F in a real vector space V and characterize the k-nondegeneracy of M in terms of the real affine geometry of F. We give a method for an explicit computation of the…
We establish that for any proper action of a Lie group on a manifold the associated equivariant differentiable cohomology groups with coefficients in modules of $\mathcal{C}^\infty$-functions vanish in all degrees except than zero.…
An almost para-CR structure on a manifold $M$ is given by a distribution $HM \subset TM$ together with a field $K \in \Gamma({\rm End}(HM))$ of involutive endomorphisms of $HM$. If $K$ satisfies an integrability condition, then $(HM,K)$ is…
We study real-analytic Levi degenerate hypersurfaces M in complex manifolds of dimension 3, for which the CR-automorphism group Aut(M) is a real Lie group acting transitively on M. We provide large classes of examples for such M, compute…