Amruthalakshmi, M.R.; Prakasha, D.G.; Bin Turki, Nasser; Unal, Inan

In this paper, we study α-cosymplectic manifold M admitting ∗-Ricci tensor. First, it is shown that a ∗-Ricci semisymmetric manifold M is ∗-Ricci flat and a φ-conformally flat manifold M is an η-Einstein manifold. Furthermore, the ∗-Weyl curvature tensor W∗ on M has been considered. Particularly, we show that a manifold M with vanishing ∗-Weyl curvature tensor is a weak φ-Einstein and a manifold M fulfilling the condition RE1,E2⋅W∗=0 is η-Einstein manifold. Finally, we give a characterization for α-cosymplectic manifold M admitting ∗-Ricci soliton given as to be nearly quasi-Einstein. Also, some consequences for three-dimensional cosymplectic manifolds admitting ∗-Ricci soliton and almost ∗-Ricci soliton are drawn.

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