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Cubic Model CR-Manifolds without the Assumption of Complete Nondegeneracy

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Abstract

In the paper, we study model surfaces with Hörmander numbers (2, 3) that do not satisfy the condition of complete nondegeneracy. Simple criteria are given for the finiteness of the type, holomorphic nondegeneracy, and holomorphic homogeneity. It is proved that the dimension of the automorphism group of the model surface is maximal in the class of germs subordinated to the surface, and also that this group is a Lie subgroup of the Cremona group. We consider the case of a surface with a unique Hörmander number 3 separately.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, 119991, Vorob’evy Gory, Moscow, Russia

    V. K. Beloshapka

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  1. V. K. Beloshapka
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Correspondence to V. K. Beloshapka.

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Beloshapka, V.K. Cubic Model CR-Manifolds without the Assumption of Complete Nondegeneracy. Russ. J. Math. Phys. 25, 148–157 (2018). https://doi.org/10.1134/S1061920818020024

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