Pelova, Galina B. Some generalizations of tensors for manifolds equipped with \(\pi\)- structures. (Bulgarian. English summary) Zbl 0626.53023 Mathematics and education in mathematics, Proc. 16th Spring Conf., Sunny Beach/Bulg. 1987, 255-259 (1987). [For the entire collection see Zbl 0619.00003.] A generalized curvature tensor and a generalized Bochner curvature tensor for manifolds with \(\pi\)-structures are considered (a \(\pi\)-structure is defined by a complex tensor field F of type (1,1) such that \(F^ 2=a^ 2I\) where a is a nonzero complex number). Some properties for these tensors are found. The manifolds equipped with a \(\pi\)-structure with certain linear relations between the sectional curvature, the generalized Ricci tensor and the metric tensor are classified. Reviewer: G.Stanilov MSC: 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) 53B35 Local differential geometry of Hermitian and Kählerian structures Keywords:curvature tensor; Bochner curvature tensor; manifolds with \(\pi \)- structures Citations:Zbl 0619.00003 PDFBibTeX XML