Affine homogeneity of indefinite real hypersurfaces in the space \(\mathbb C^{3}\)
The authors develop a constructive approach to the problem of describing affinely homogeneous real hypersurfaces in 3-dimensional complex space having nondegenerate sign-indefinite Levi form. They construct the affine invariants of a nondegenerate indefinite hypersurface in terms of second-order jets of its defining function and introduce the notion of the affine canonical equation of this surface. Three main types of canonical equations are considered. For each of these types, the authors construct a family of Lie algebras related to affinely homogeneous surfaces of a particular type. As a result, a family (depending on two real parameters) of affinely different homogeneous submanifolds of 3-dimensional complex space is presented in the form of matrix algebras.
affinely homogeneous indefinite hypersurface
canonical equation of an indefinite surface
scientific article; zbMATH DE number 5980727
scientific article