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On weakly \(W_3\)-symmetric manifolds. (English) Zbl 1252.53020
The object of the paper under review is to study weakly \(W_3\)-symmetric manifolds and its decomposability with the existence of such notions. Among others it is shown that in a decomposable weakly \(W_3\)-symmetric manifold both decompositions are weakly Ricci symmetric.

MSC:
53B05 Linear and affine connections
53B35 Local differential geometry of Hermitian and Kählerian structures
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
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