Abstract:
Homogeneous model submanifolds of $\mathrm{CR}$-type $(1, 3)$ in the complex space $\mathbb C^4$ are investigated. In the course of the study, the moduli space of five-dimensional model surfaces of the Bloom–Graham type $((2, 1),(3, 1),(4, 1))$ are found. It is also shown that, among the model surfaces of this type, exactly one surface has the property of holomorphic homogeneity, which is equivalent to the tubular surface $\mathcal {C}$ over an affinely homogeneous curve in $\mathbb R ^4$. The paper describes a family of six-dimensional holomorphically homogeneous surfaces obtained as orbits of the action of the group of holomorphic automorphisms of $\mathcal C$ and classifies them from the point of view of the corresponding model surfaces.
Keywords:$\mathrm{CR}$-manifold, holomorphically homogeneous manifold, model surface,
Bloom–Graham type.
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