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On a class of generalized quasi-Einstein manifolds. (English) Zbl 1103.53023

A necessary condition is proved for a generalized quasi-Einstein manifold, with parallel generators, to be either Ricci pseudo-symmetric, \(R\)-harmonic or with cyclic-parallel Ricci tensor.

MSC:

53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
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