A Quasiperiodic System of Polynomial Models of CR-Manifolds

Polynomial models for the germs of real submanifolds of a complex space are constructed. For the germs whose Levi–Tanaka algebra has length 2, such a sufficiently well-studied model is given by a tangent quadric. It is shown that models of the third and fourth degrees (algebras of lengths 3 and 4) possess, in their codimension ranges, a full spectrum of properties that are completely analogous to the properties of tangent quadrics. For the constructed higher order models, a full spectrum of properties is obtained with the only exception that they are not fully universal.