CR-Manifolds of Finite Bloom–Graham Type: the Model Surface Method

Abstract

In the paper, the model surface method is applied to arbitrary CR-manifolds of finite Bloom–Graham type. A family of basic assertions is proved. It is proved also that, for a model surface, the condition that the Bloom–Graham type is constant is a criterion for holomorphic homogeneity. Distinctions from the case of rigid models treated earlier are clarifies. A series of questions and conjectures is formulated.