Some geometric properties of η Ricci solitons and gradient Ricci solitons on (lcs) n -manifolds
Sunil Yadav,S. K. Chaubey,D. L. Suthar +2 more
- Vol. 19, Iss: 2, pp 33–48-33–48
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In this article, the existence of Ricci solitons on a (LCS)-manifold (M, ϕ, ξ, η, g) is shown to imply quasi-Einstein.Abstract:
In the context of para-contact Hausdorff geometry η−Ricci solitons and gradient Ricci solitons are considered on manifolds. We establish that on an (LCS)𝑛−manifold (M, ϕ, ξ, η, g), the existence of an η−Ricci soliton implies that (M, g) is quasi-Einstein. We find conditions for Ricci solitons on an (LCS)𝑛−manifold (M, ϕ, ξ, η, g) to be shrinking, steady and expanding. At the end we show examples of such manifolds with η−Ricci solitons.read more
Citations
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Journal ArticleDOI
Certain results for η-Ricci Solitons and Yamabe Solitons on quasi-Sasakian 3-Manifolds
TL;DR: In this article, the authors classify quasi-Sasakian 3-manifold with proper Ricci soliton and investigate its geometrical properties, and construct an example of non-existence of proper η-Ricci solitons on 3-dimensional quasi-sakian manifold.
Some Results on (LCS ) 2 n+1 -Manifolds
TL;DR: In this paper, the authors classify Lorentzian concircular structure manifolds (briefly (LCS) 2n+1 -manifold) admitting a W2 - curvature tensor and obtain some interesting results.
Some results of η-Ricci solitons on (LCS) n -manifolds
TL;DR: In this article, the existence of Ricci solitons on the (LCS)n-manifolds satisfying certain curvature conditions was studied and it was shown that the Ricci-soliton is a quasi-Einstein soliton.
Journal ArticleDOI
Some Ricci solitons on Kenmotsu manifold
B. Shanmukha,V. Venkatesha +1 more
TL;DR: In this paper, the authors studied the properties of the Ricci soliton on the Kenmotsu manifold and also analyzed the generalized gradient RICCI soliton equation satisfying some conditions.
Journal ArticleDOI
Anti-Invariant Lorentzian Submersions From Lorentzian Concircular Structure Manifolds
TL;DR: In this article , it was shown that the horizontal distributions of the Lagrangian Lorentzian submersions are not integrable and their fibers are not totally geodesic.
References
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Semi-Riemannian Geometry With Applications to Relativity
TL;DR: In this article, the authors introduce Semi-Riemannian and Lorenz geometries for manifold theory, including Lie groups and Covering Manifolds, as well as the Calculus of Variations.
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Hamilton's Ricci Flow
Bennett Chow,Peng Lu,Lei Ni +2 more
TL;DR: Riemannian geometry and singularity analysis of Ricci flow have been studied in this paper, where Ricci solitons and special solutions have been used for geometric flows.
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Transverse Kähler geometry of Sasaki manifolds and toric Sasaki-Einstein manifolds
TL;DR: In this article, the existence of transverse Kahler-Ricci solitons on compact toric Sasaki manifolds was shown to be an obstruction to the transverse KG metric with harmonic Chern forms.
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