Abstract
The action on the space \(\mathbb C^4\) of the 7-dimensional Lie group of infinitesimal holomorphic automorphisms of a completely nondegenerate cubic model surface \(Q\) of CR-type \((1,3)\) is considered. All orbits of the given action are found and their biholomorphic classification is given. One of the orbits coincides with the surface \(Q\) (the 5-dimensional orbit), two orbits are 6-dimensional, and the remaining part of the space \(\mathbb C^4\), the complement to the above orbits, foliates into 7-dimensional real orbits. It is also proved that the algebra of infinitesimal holomorphic automorphisms of all orbits, except for the twelve holomorphically degenerate orbits, coincides with the algebra of the surface \(Q\).
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Acknowledgments
The present paper arose as a continuation of the joint discussions that both authors conducted in September of 2019 at the Isfahan branch of IPM, where the first author was invited by the Directorate of the Institute. The first author is grateful to the Direction of the Isfahan branch of IPM for the provided opportunity and hospitality. We are also grateful to Amir Hashemi, Mehdi Dehgani and Maria Stepanova for helpful comments and discussions during the work on the paper.
Funding
The research of the first author was supported by the Russian Science Foundation under grant no. 18-41-05003. The research of the second author was partially supported by the IPM grant no. 99510419.
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Beloshapka, V.K., Sabzevari, M. Homogeneous Surfaces in \(\mathbb C^4\) Associated with a 5-Dimensional Completely Nondegenerate Cubic Model Surface of CR-Type \((1,3)\). Russ. J. Math. Phys. 27, 424–432 (2020). https://doi.org/10.1134/S1061920820040020
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DOI: https://doi.org/10.1134/S1061920820040020