On Special Weakly Ricci-Symmetric Kenmotsu Manifolds
DOI:
https://doi.org/10.5644/SJM.03.1.09Keywords:
Kenmotsu manifold, special weakly Ricci-symmetric manifold, Einstein manifoldAbstract
In this paper, we have studied special weakly Ricci symmetric Kenmotsu manifolds. We show that if a special weakly Riccisymmetric Kenmotsu manifold admits a cyclic parallel Ricci tensor then the associate 1–form $\alpha$ must be zero. On the other hand we show that a special weakly Ricci-symmetric Kenmotsu manifold can not be an Einstein manifold if the associate 1–form $\alpha$ $\neq$ 0 and Ricci tensor of a special weakly Ricci-symmetric Kenmotsu manifold is parallel.
2000 Mathematics Subject Classification. 53C21, 53C25
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