Generalized quasi-Kählerian manifolds and axioms of CR-submanifolds in generalized Hermitian geometry. I
The axiom of planes and of holomorphic planes are generalized here by the so-called axiom of CR-submanifolds. Generalized quasi-Kählerian manifolds are studied. The results of \textit{A. Gray} and \textit{L. Vanhecke} [Čas. Peštovani Mat. 104, 170-179 (1979; Zbl 0413.53011)] as well as \textit{A. M. Naveira} and \textit{L. M. Hervella} [Proc. Am. Math. Soc. 49, 421-425 (1975; Zbl 0282.53021)] for nearly Kähler manifolds are generalized here. A complete classification of split reductive generalized nearly Kählerian manifolds of constant holomorphic sectional curvature is obtained.
scientific article; zbMATH DE number 663735
scientific article