∗-Ricci Tensor on α-Cosymplectic Manifolds. (21st February 2022) - Amruthalakshmi, M. R.; Prakasha, D. G.; Bin Turki, Nasser; Unal, Inan
Abstract : 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 R E 1, E 2 ⋅ 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.