Automorphism Groups of Normal Cr 3-manifolds

Cr Manifolds with Noncompact Connected Automorphism Groups

The main result of this paper is that the identity component of the automorphism group of a compact, connected, strictly pseudoconvex CR manifold is compact unless the manifold is CR equivalent to the standard sphere. In dimensions greater than 3, it has been pointed out by D. Burns that this result follows from known results on biholomorphism groups of complex manifolds with boundary and the f...

CR-manifolds of dimension 5: A Lie algebra approach

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 the corresponding groups Aut(M) and determine the maximal subsets of M that cannot be separated by global continuous CR-functions. It turns out that all our ...

Automorphism Groups of Normal Cr 3 - Manifoldsflorin

/lhjurxsvwuxfwxuhvrqdxwrprusklvpjurxsvriuhdodqdo\wlf &5pdqlirogv Lie Group Structures on Automorphism Groups of Real-analytic Cr Manifolds

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 AutCR (M) is a Lie group (in an appropriate topology). In particular, we obtain a Lie group structure for AutCR (M) when M is an arbitrary compact real-analytic hypersurface embedded in some Stein manifold.

Normal Cr Structures on Compact 3-manifolds

We study normal CR compact manifolds in dimension 3. For a choice of a CR Reeb vector field, we associate a Sasakian metric on them, and we classify those metrics. As a consequence, the underlying manifolds are topologically finite quotiens of S or of a circle bundle over a Riemann surface of positive genus. In the latter case, we prove that their CR automorphisms group is a finite extension of...