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Three-dimensional positively curved generalized Ricci solitons with SO(3)-symmetries
Advances in MathematicsWe prove the existence of a one-parameter family of pairwise non-isometric, complete, positively curved, steady generalized Ricci solitons of gradient type on $\mathbb{R}^3$ that are invariant under the natural cohomogeneity one action of SO(3).
F. Podestà, Alberto Raffero
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Chinese Annals of Mathematics, Series B, 2006
This paper is a survey of recent developments on Ricci solitons. \ A Ricci soliton is a complete Riemannian metric \(g_{ij}\) on a manifold \(M\) having a vector field \(V\) and constant \(\rho \) so that the Ricci tensor satisfies \(2R_{ij}+\nabla _{i}V_{j}+\nabla _{j}V_{i}=2\rho g_{ij}.\) These are generalization of Einstein metrics.
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This paper is a survey of recent developments on Ricci solitons. \ A Ricci soliton is a complete Riemannian metric \(g_{ij}\) on a manifold \(M\) having a vector field \(V\) and constant \(\rho \) so that the Ricci tensor satisfies \(2R_{ij}+\nabla _{i}V_{j}+\nabla _{j}V_{i}=2\rho g_{ij}.\) These are generalization of Einstein metrics.
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CLASSES OF GRADIENT RICCI SOLITONS
International Journal of Geometric Methods in Modern Physics, 2011We introduce a study of Riemannian manifold M = ℝ2 endowed with a metric of diagonal type of the form [Formula: see text], where g is a positive function, of C∞-class, depending on the variable x2 only. We emphasize the role of metric [Formula: see text] in determining manifolds having negative, null or positive sectional curvature.
Bercu, Gabriel, Postolache, Mihai
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The Poisson equation on compact Ricci solitons and Ricci-harmonic solitons
Journal of Geometry, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Geometry and analysis of gradient Ricci solitons in dimension four
Surveys in Differential Geometry[Dedicated to Richard S. Hamilton on forty years of Ricci flow] Gradient Ricci solitons have garnered significant attention both as self-similar solutions and singularity models of the Ricci flow.
Xiaodong Cao, Hung Tran
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A note on almost Ricci solitons
Analysis and Mathematical Physics, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sharief Deshmukh, Hana Al-Sodais
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CONTACT GEOMETRY AND RICCI SOLITONS
International Journal of Geometric Methods in Modern Physics, 2010We show that a compact contact Ricci soliton with a potential vector field V collinear with the Reeb vector field, is Einstein. We also show that a homogeneous H-contact gradient Ricci soliton is locally isometric to En+1 × Sn(4). Finally we obtain conditions so that the horizontal and tangential lifts of a vector field on the base manifold may be ...
Cho, Jong Taek, Sharma, Ramesh
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Ricci Solitons and Paracontact Geometry
Mediterranean Journal of Mathematics, 2019The present paper concerns Ricci solitons in the setting of paracontact metric geometry. A reduction result to Einstein or \(\eta \)-Einstein metrics is obtained in Theorem 10. The \(K\)-paracontact condition yields the expanding character of the soliton and the constancy of the scalar curvature. Also, \((k, \mu )\)-paracontact manifolds are considered.
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GEOMETRY OF THE RICCI SOLITON HYPERSURFACES
JP Journal of Geometry and Topology, 2016Summary: In this paper, we investigate the geometry of the Ricci soliton hypersurface \((M,g,f,\lambda)\) in a Euclidean space. We find sufficient conditions first for this Ricci soliton hypersurface to be totally geodesic and to be isometric to a sphere. We also study two special cases, when the mean curvature is constant and when the scalar curvature
Alsodais, Hana, Alodan, Haila
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η-Ricci solitons and almost η-Ricci solitons on para-Sasakian manifolds
International Journal of Geometric Methods in Modern Physics, 2019In this paper, we study para-Sasakian manifold [Formula: see text] whose metric [Formula: see text] is an [Formula: see text]-Ricci soliton [Formula: see text] and almost [Formula: see text]-Ricci soliton. We prove that, if [Formula: see text] is an [Formula: see text]-Ricci soliton, then either [Formula: see text] is Einstein and in such a case the ...
Naik, Devaraja Mallesha, Venkatesha, V.
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