Generalized quasi-Kaehlerian manifolds and axioms of CR-submanifolds in generalized Hermitian geometry. II
This paper is continuation of [ibid. 51, No. 1, 75-104 (1994; Zbl 0817.53016)] and is dedicated to the study of the geometry of generalized quasi-Kählerian (GQK) and generalized nearly-Kählerian (GNK) manifolds. Concerning GQK manifolds, the author studies their structural equations, the \(Q\)-spaces, the GQK manifolds of constant holomorphic sectional curvature, and finally splittable reductive GQK manifolds satisfying the axiom of CR-spheres which is the key topic of the paper. In the field of GNK manifolds, the general properties of these manifolds, the holomorphic non-reducible GNK manifolds and the GNK manifolds of constant holomorphic sectional curvature are considered. The main result of the paper is Theorem 38 which states: A splittable reductive GQK-manifold of dimension greater than 4 satisfying the axiom of CR-spheres of type \((\alpha, \beta)\) is locally equivalent to one of the following manifolds: 1) A complex pseudo-Euclidean space; 2) a complex pseudo-projective space; 3) a complex pseudo-hyperbolic space; 4) a double Euclidean space; 5) a manifold of null pairs of real projective space; 6) the product of manifolds of types 1 and 4; 7) a 6-dimensional oriented manifold of constant curvature, positive in case of a positively definite metric and equipped with a canonical nearly Kählerian structure or its hyperbolic counterpart.
scientific article; zbMATH DE number 679554
scientific article