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Ricci soliton and Ricci almost soliton within the framework of Kenmotsu manifold
Karpatsʹkì Matematičnì Publìkacìï, 2019 First, we prove that if the Reeb vector field $\xi$ of a Kenmotsu manifold $M$ leaves the Ricci operator $Q$ invariant, then $M$ is Einstein. Next, we study Kenmotsu manifold whose metric represents a Ricci soliton and prove that it is expanding ...
A. Ghosh
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Frontiers in Physics, 2022 The goal of the present study is to study the ∗-η-Ricci soliton and gradient almost ∗-η-Ricci soliton within the framework of para-Kenmotsu manifolds as a characterization of Einstein metrics.
Santu Dey, Nasser Bin Turki
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Uniqueness of Kähler-Ricci solitons [PDF]
Acta Mathematica, 2000 Let \(X\) be a holomorphic vector field on a compact Kähler manifold \((M,\omega)\). Then \(\omega\) is a Kähler-Ricci soliton with respect to \(X\) if \(\text{Ric} (\omega)-\omega=L_X\omega\) where \(\text{Ric} (\omega)\) is the Ricci form and \(L_X\) is the Lie derivative with respect to \(X\).
Gang Tian, Xiaohua Zhu
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AIMS MathematicsIn this research note, we investigated the characteristics of perfect fluid spacetime when coupled with the hyperbolic Ricci soliton. We additionally interacted with the perfect fluid spacetime, with a $ \varphi(\mathcal{Q}) $-vector field and a bi ...
Mohd. Danish Siddiqi , Fatemah Mofarreh
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Homogeneous Ricci solitons [PDF]
Journal für die reine und angewandte Mathematik (Crelles Journal), 2011 Abstract In this work, we study metrics which are both homogeneous and Ricci soliton. If there exists a transitive solvable group of isometries on a Ricci soliton, we show that it is isometric to a solvsoliton. Moreover, unless the manifold is flat, it is necessarily simply-connected and diffeomorphic to ℝ n
R Lafuente, Jorge Lauret
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Characterizations of Trivial Ricci Solitons [PDF]
Advances in Mathematical Physics, 2020 Finding characterizations of trivial solitons is an important problem in geometry of Ricci solitons. In this paper, we find several characterizations of a trivial Ricci soliton.
Sharief Deshmukh +2 more
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On homogeneous Ricci solitons [PDF]
The Quarterly Journal of Mathematics, 2012 We study the evolution of homogeneous Ricci solitons under the bracket flow, a dynamical system on the space of all homogeneous spaces of dimension n with a q-dimensional isotropy, which is equivalent to the Ricci flow for homogeneous manifolds. We prove that algebraic solitons (i.e.
R Lafuente, Jorge Lauret
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On Ricci solitons of cohomogeneity one [PDF]
Annals of Global Analysis and Geometry, 2008 We analyse some properties of the cohomogeneity one Ricci soliton equations, and use Ansatze of cohomogeneity one type to produce new explicit examples of complete Kahler Ricci solitons of expanding, steady and shrinking types. These solitons are foliated by hypersurfaces which are circle bundles over a product of Fano Kahler-Einstein manifolds or over
Andrew Dancer, McKenzie Y. Wang
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Degeneration of Shrinking Ricci Solitons [PDF]
International Mathematics Research Notices, 2010 Let $(Y,d)$ be a Gromov-Hausdorff limit of closed shrinking Ricci solitons with uniformly upper bounded diameter and lower bounded volume. We prove that off a closed subset of codimension at least 2, $Y$ is a smooth manifold satisfying a shrinking Ricci soliton equation.
Zuo‐Feng Zhang
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The curvature of gradient Ricci solitons [PDF]
Mathematical Research Letters, 2011 We study integral and pointwise bounds on the curvature of gradient shrinking Ricci solitons. As applications we discuss gap and compactness results for gradient shrinkers.
Ovidiu Munteanu, Mu‐Tao Wang
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