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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

Citations:

Zbl 0619.00003