∗-Ricci Tensor on α-Cosymplectic Manifolds. (21st February 2022)

• Record Type: Journal Article
• Authors: Amruthalakshmi, M. R.; Prakasha, D. G.; Bin Turki, Nasser; Unal, Inan
• Other Names: Khan Meraj Ali Academic Editor.
• Is Part Of: Advances in mathematical physics. Volume 2022(2022)
• Publication Date: 2022-02-21
• Subjects: Mathematical physics -- Periodicals; Mathematical physics; Periodicals; 530.15
• DOI: 10.1155/2022/7939654
• Languages: English
• ISSNs: 1687-9120

Abstract

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.