∗-Ricci Tensor on α-Cosymplectic Manifolds
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...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2022/7939654 |
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| Summary: | 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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| ISSN: | 1687-9139 |