∗-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...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
|
| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2022/7939654 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832550407893680128 |
|---|---|
| author | M. R. Amruthalakshmi D. G. Prakasha Nasser Bin Turki Inan Unal |
| author_facet | M. R. Amruthalakshmi D. G. Prakasha Nasser Bin Turki Inan Unal |
| author_sort | M. R. Amruthalakshmi |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-38774120be1d47ad9abec6dee68fa30b |
| institution | Kabale University |
| issn | 1687-9139 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-38774120be1d47ad9abec6dee68fa30b2025-02-03T06:06:47ZengWileyAdvances in Mathematical Physics1687-91392022-01-01202210.1155/2022/7939654∗-Ricci Tensor on α-Cosymplectic ManifoldsM. R. Amruthalakshmi0D. G. Prakasha1Nasser Bin Turki2Inan Unal3Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of Computer EngineeringIn 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.http://dx.doi.org/10.1155/2022/7939654 |
| spellingShingle | M. R. Amruthalakshmi D. G. Prakasha Nasser Bin Turki Inan Unal ∗-Ricci Tensor on α-Cosymplectic Manifolds Advances in Mathematical Physics |
| title | ∗-Ricci Tensor on α-Cosymplectic Manifolds |
| title_full | ∗-Ricci Tensor on α-Cosymplectic Manifolds |
| title_fullStr | ∗-Ricci Tensor on α-Cosymplectic Manifolds |
| title_full_unstemmed | ∗-Ricci Tensor on α-Cosymplectic Manifolds |
| title_short | ∗-Ricci Tensor on α-Cosymplectic Manifolds |
| title_sort | ∗ ricci tensor on α cosymplectic manifolds |
| url | http://dx.doi.org/10.1155/2022/7939654 |
| work_keys_str_mv | AT mramruthalakshmi riccitensoronacosymplecticmanifolds AT dgprakasha riccitensoronacosymplecticmanifolds AT nasserbinturki riccitensoronacosymplecticmanifolds AT inanunal riccitensoronacosymplecticmanifolds |