Almost complex and almost contact structures in fibred Riemannian spaces
Relations among structures of fibre spaces [cf. e.g. \textit{S. Ishihara} and \textit{M. Konishi}, Differential geometry of fibred spaces (Tokyo 1973; Zbl 0337.53001)] with almost Hermitian or almost contact metric structures and those of base spaces and fibres are studied. In particular, a condition for a fibred almost Hermitian space with anti- invariant fibres to be Kählerian is obtained. Conditions for a fibred almost contact metric space to be contact metric as well as Sasakian are found. Moreover, certain applications to tangent bundles of Riemannian spaces and almost contact metric spaces are given.
scientific article; zbMATH DE number 4069741