On complete list of affine homogeneous surfaces of (ɛ, 0)-types in the space ℂ3

Abstract

The problem of description of affine homogeneous real hypersurfaces in complex spaces is an important part of the problem of holomorphic classification of homogeneous manifolds, which has no complete solution till now, even in the 3-dimensional case. The method developed by the authors, based on affine canonical equations and techniques of matrix Lie algebras, allowed them earlier to obtain complete descriptions of two natural classes of affine homogeneous real hypersurfaces in the 3-dimensional complex space. In this paper, we present the complete description of one more class. The description includes examples already known and (obtained with the use of symbolic computations) Lie algebras corresponding to the other homogeneous manifolds belonging to the types under consideration. The main result of the paper is obtained by means of integration of these algebras.