Generalized quasi-Kaehlerian manifolds and axioms of CR-submanifolds in generalized Hermitian geometry. II
type: Item
instance of: scholarly article
title: Generalized quasi-Kaehlerian manifolds and axioms of CR-submanifolds in generalized Hermitian geometry. II
zbMATH Open document ID: 0836.53042
DOI: 10.1007/BF01263524
author: V. F. Kirichenko
published in: Geometriae Dedicata
publication date: 1996-04-16T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 679554
zbMATH Keywords: generalized quasi-Kähler manifolds
zbMATH Keywords: CR-submanifolds
zbMATH Keywords: generalized nearly-Kähler manifolds
MaRDI profile type: Publication
cites work: Q3943626
cites work: Q5830179
cites work: Q4098867
cites work: Some examples of almost Hermitian manifolds
cites work: The structure of nearly Kähler manifolds
cites work: Classification of a conformally flat K-space
cites work: Nearly Kähler manifolds
cites work: On the existence of analytic mappings
cites work: Q5646076
cites work: Q3726941
cites work: Q4746404
cites work: Differential-geometric structures on manifolds
cites work: Q5665876
cites work: Q3346895
cites work: Q5613049
Recommended article: Generalized quasi-Kählerian manifolds and axioms of CR-submanifolds in generalized Hermitian geometry. I
Recommended article: Q3172728
Recommended article: On hypersurfaces of generalized Kähler manifolds
Recommended article: Q2997540
Recommended article: Generic submanifolds of nearly Kähler manifolds with certain parallel canonical structure
Recommended article: On Kähler-like and G-Kähler-like quasi-Kähler manifolds
Recommended article: Kähler manifolds of quasi-constant holomorphic sectional curvature and generalized Sasakian space forms
Recommended article: Q3517505
Recommended article: A note on submanifolds of generalized K\"ahler manifolds
Recommended article: Generalized Kähler manifolds, commuting complex structures, and split tangent bundles
description: scientific article; zbMATH DE number 679554