A note on almost co-Kähler manifolds
26 Aug 2020-International Journal of Geometric Methods in Modern Physics (World Scientific Publishing Company)-Vol. 17, Iss: 10, pp 2050153
TL;DR: In this paper, it was shown that the metric of a (κ,μ)-almost co-Kahler manifold M2n+1 is a gradieness of a quasi-Yamabe solitons.
Abstract: We characterize almost co-Kahler manifolds with gradient Yamabe, gradient Einstein and quasi-Yamabe solitons. It is proved that if the metric of a (κ,μ)-almost co-Kahler manifold M2n+1 is a gradien...
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TL;DR: In this paper, it was shown that the Weyl tensor is divergence-free and the potential function of the concircular vector field is pointwise collinear with the velocity vector field of perfect fluid spacetime.
Abstract: This paper deals with the study of perfect fluid spacetimes. It is proven that a perfect fluid spacetime is Ricci recurrent if and only if the velocity vector field of perfect fluid spacetime is parallel and α = β. In addition, in a stiff matter perfect fluid Yang pure space with p + σ ≠ 0, the integral curves generated by the velocity vector field are geodesics. Moreover, it is shown that in a generalized Robertson–Walker perfect fluid spacetime, the Weyl tensor is divergence-free and the gradient of the potential function of the concircular vector field is pointwise collinear with the velocity vector field of perfect fluid spacetime. We also characterize the perfect fluid spacetimes whose Lorentzian metrics are Yamabe and gradient Yamabe solitons, respectively.
22 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.
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TL;DR: In this article , the existence of ∗ - η -Ricci-Yamabe solitons in a 5-dimensional Sasakian manifold has been proved through a concrete example.
Abstract: In this note, we characterize Sasakian manifolds endowed with ∗ - η -Ricci-Yamabe solitons. Also, the existence of ∗ - η -Ricci-Yamabe solitons in a 5-dimensional Sasakian manifold has been proved through a concrete example.
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08 Jan 2002
TL;DR: In this article, the authors describe a complex geometry model of Symplectic Manifolds with principal S1-bundles and Tangent Sphere Bundles, as well as a negative Xi-sectional Curvature.
Abstract: Preface * 1. Symplectic Manifolds * 2. Principal S1-bundles * 3. Contact Manifolds * 4. Associated Metrics * 5. Integral Submanifolds and Contact Transformations * 6. Sasakian and Cosymplectic Manifolds * 7. Curvature of Contact Metric Manifolds * 8. Submanifolds of Kahler and Sasakian Manifolds * 9. Tangent Bundles and Tangent Sphere Bundles * 10. Curvature Functionals and Spaces of Associated Metrics * 11. Negative Xi-sectional Curvature * 12. Complex Contact Manifolds * 13. Additional Topics in Complex Geometry * 14. 3-Sasakian Manifolds * Bibliography * Subject Index * Author Index
1,822 citations
TL;DR: In this article, the fundamental collineation of the almost complex structure of differentiable manifold with almost complex structures has been studied, where the set of manifold with complex structures is wider than the set with complex structure.
Abstract: then M is said to be a differentiable manifold with almost complex structure. (Tensor fields of the form given above may exist only for some manifolds with even dimension.) We shall call φ the fundamental collineation of the almost complex structure. The set of differentiable manifolds with almost complex structure is wider than the set of complex manifolds. Every differentiable manifold with almost complex structure φ admits a poistive definite Riemannian metric g such that
427 citations
213 citations
129 citations