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

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

2009-10-05

arxiv.org/abs/0910.0658v1

Mathematics

Complex Variables

Scientific paper

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 $\CC{3}$.

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