arXiv subjects

I. G. Kossovskiy

Publications and source records attributed to I. G. Kossovskiy.

3 recordsLinked to original sources

arXiv2009

Classification of homogeneous CR-manifolds in dimension 4

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 also to classify all symmetric CR-manifolds in dimension 4, up to local biholomorphic equivalence. We also prove that any 4-dimensional real Lie algebra can be realized as an algebra of affine vector fields in a domain in $\CC{3}$, linearly independent at each point.

math.CV↗

arXiv2009

Homogeneous hypersurfaces in $\CC{3}$, associated with a model CR-cubic

The model 4-dimensional CR-cubic in $\CC{3}$ has the following "model" property: it is (essentially) the unique locally homogeneous 4-dimensional CR-manifold in $\CC{3}$ with finite-dimensional infinitesimal automorphism algebra $\mathfrak{g}$ and non-trivial isotropy subalgebra. We study and classify, up to local biholomorphic equivalence, all $\mathfrak{g}$-homogeneous hypersurfaces in $\CC{3}$ and also classify the corresponding local transitive actions of the model algebra $\mathfrak{g}$ on hypersurfaces in $\CC{3}$.

math.CV↗

arXiv2009

Continuation of CR-Automorphisms of Levi Degenerate Hyperquadrics to the Projective Space

We show that every CR-automorphism of the closure of a Levi degenerate hyperquadric in the projective space extends to a holomorphic automorphism of the projective space.

math.CV↗