Erratum: Aberrant CR structures

Normal Forms for Non-integrable Cr Structures

1 2 D. ZAITSEV

Normal Forms for Nonintegrable Almost Cr Structures

We propose two constructions extending the Chern-Moser normal form to non-integrable Levi-nondegenerate (hypersurface type) almost CR structures. One of them translates the ChernMoser normalization into pure intrinsic setting, whereas the other directly extends the (extrinsic) Chern-Moser normal form by allowing non-CR embeddings that are in some sense “maximally CR”. One of the main difference...

A combinatorial invariant for Spherical CR structures

We study a cross-ratio of four generic points of S which comes from spherical CR geometry. We construct a homomorphism from a certain group generated by generic configurations of four points in S to the pre-Bloch group P(C). If M is a 3-dimensional spherical CR manifold with a CR triangulation, by our homomorphism, we get a P(C)-valued invariant for M . We show that when applying to it the Bloc...

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...

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