Abstract
The problem of describing affine homogeneous real hypersurfaces of the complex space C3 was posed in [1]. Such an affine setting is closely related to the problem of classifying holomorphically homogeneous submanifolds of multidimensional complex spaces (see [2]–[4]). A scheme for the study of the affine homogeneity property based on the use of the canonical equations of the manifolds under consideration was proposed in [5]–[7]. The scheme envisages a separate study of several (for example, seven) types of strictly pseudoconvex hypersurfaces depending on the second-order Taylor coefficients of their canonical equations. This scheme was used in [6]–[8] to give a complete description of two of the seven cases mentioned above. Below we describe the third possible type.
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