Model CR-manifolds with one-dimensional complex tangent

Abstract

In the paper, the groups of holomorphic automorphisms of model surfaces of types (1,8), (1,9), ..., (1,12) are studied. This completes the investigation of automorphisms of the model surfaces with one-dimensional complex tangent whose Levi-Tanaka algebra is of length not exceeding five. As a corollary, the following assertion is proved: the graded Lie algebra of infinitesimal holomorphic symmetries of a model surface of type (1,K) has no positive component for any K, 2 ⩽ K ⩽ 12. This is another confirmation, after Kossovskii’s theorem, of the Beloshapka conjecture on the rigidity of model surfaces.