On quasi-Sasakian 3-manifolds admitting η-Ricci solitons
TL;DR: In this paper, it was shown that in a quasi-Sasakian 3-manifold admitting Ricci soliton, the structure function is a constant, which is the same as in the present paper.
Abstract: The object of the present paper is to prove that in a quasi-Sasakian
3-manifold admitting ?-Ricci soliton, the structure function ? is a
constant. As a consequence we obtain several important results.
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TL;DR: In this article , the existence of Ricci solitons in LP-Kenmotsu manifolds in the spacetime of general relativity has been proved through a nontrivial example.
Abstract: In the present paper, -Kenmotsu manifolds admitting -Ricci solitons have been studied. Moreover, some results for -Ricci solitons in LP-Kenmotsu manifolds in the spacetime of general relativity have also been proved. Through a nontrivial example, we have given a proof for the existence of η-Ricci solitons in a 5-dimensional LP-Kenmotsu manifold.
12 citations
TL;DR: In this paper, the authors characterize the gradient Yamabe and the gradient m-quasi Einstein solitons within the framework of three-dimensional cosymplectic manifolds.
Abstract: In this paper, we characterize the gradient Yamabe and the gradient m-quasi Einstein solitons within the framework of three-dimensional cosymplectic manifolds.
11 citations
TL;DR: In this article, it was shown that a 3D Riemannian manifold endowed with a semi-symmetric ρ-connection, whose metric is a Yamabe soliton, is a manifold of constant sectional curvature − 1 and the soliton is expanding with soliton constant − 6.
11 citations
TL;DR: In this article, the properties of perfect fluid spacetimes endowed with the gradient η -Ricci and gradient Einstein solitons were studied, and the authors set the goal to study the properties.
11 citations
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TL;DR: In this paper, a family of quasi-Einstein metrics with an isometry group U(n) acting linearly on the holomorphic coordinates is constructed, and suitable restrictions on the parameters give rise to complete non-compact as well as compact metrics whose geometrical structure is studied in detail.
62 citations
"On quasi-Sasakian 3-manifolds admit..." refers background in this paper
...Metrics satisfying (1) are interesting and useful in physics and are often referred as quasi-Einstein ([12],[13])....
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TL;DR: In this paper, the authors classify locally homogeneous quasi-Sasakian manifolds in dimension five that admit a parallel spinor of algebraic type $F \cdot \psi = 0$ with respect to the unique connection preserving the quasi-sakian structure and with totally skew symmetric torsion.
Abstract: We classify locally homogeneous quasi-Sasakian manifolds in dimension five that admit a parallel spinor $\psi$ of algebraic type $F \cdot \psi = 0$ with respect to the unique connection $
abla$ preserving the quasi-Sasakian structure and with totally skew-symmetric torsion. We introduce a certain conformal transformation of almost contact metric manifolds and discuss a link between them and the dilation function in 5-dimensional string theory. We find natural conditions implying conformal invariances of parallel spinors. We present topological obstructions to the existence of parallel spinors in the compact case.
52 citations
48 citations
"On quasi-Sasakian 3-manifolds admit..." refers background in this paper
...Tanno [33] also added some remarks on quasi-Sasakian structures....
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TL;DR: In this paper, it was shown that if a 3-dimensional cosymplectic manifold M3 admits a Ricci soliton, then either M3 is locally flat or the potential vector field is an infinitesimal contact transformation.
Abstract: Abstract In this paper, we prove that if a 3-dimensional cosymplectic manifold M3 admits a Ricci soliton, then either M3 is locally flat or the potential vector field is an infinitesimal contact transformation.
34 citations
"On quasi-Sasakian 3-manifolds admit..." refers background in this paper
...Ricci solitons have been studied by several authors such as ([15], [16], [23], [24], [35], [36]) and many others....
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TL;DR: In this article, it was shown that the Ricci soliton of a three-dimensional (3D)-Einstein almost-Einstein soliton is a Ricci manifold of constant sectional curvature.
Abstract: Let the metric $g$ of a three-dimensional $\eta$-Einstein almost Kenmotsu manifold $M$ be a Ricci soliton, we prove that $M$ is a Kenmotsu manifold of constant sectional curvature $-1$ and the soliton is expanding.
33 citations
"On quasi-Sasakian 3-manifolds admit..." refers background in this paper
...Ricci solitons have been studied by several authors such as ([15], [16], [23], [24], [35], [36]) and many others....
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