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Expanding Ricci solitons with pinched Ricci curvature [PDF]

arXiv, 2010
In this paper, we prove that expanding gradient Ricci solitons with (positively) pinched Ricci curvature are trivial ones. Namely, they are either compact or flat.
Li Ma
arxiv   +7 more sources

On homogeneous Ricci solitons [PDF]

arXiv, 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
arxiv   +9 more sources

Remarks on Gradient Ricci Solitons [PDF]

arXiv, 2004
In this paper, we study the gradient Ricci soliton equation on a complete Riemannian manifold. We show that under a natural decay condition on the Ricci curvature, the Ricci soliton is Ricci-flat and ALE.
Li Ma
arxiv   +3 more sources

Back to almost Ricci solitons [PDF]

arXiv, 2023
In the paper, we study complete almost Ricci solitons using the concepts and methods of geometric dynamics and geometric analysis. In particular, we characterize Einstein manifolds in the class of complete almost Ricci solitons. Then, we examine compact almost Ricci solitons using the orthogonal expansion of the Ricci tensor, this allows us to ...
Vladimir Rovenski, Sergey Stepanov, Irina Tsyganok   +2 more
arxiv   +4 more sources

Stability and instability of Ricci solitons [PDF]

Calculus of Variations and Partial Differential Equations, 2014
We consider the volume-normalized Ricci flow close to compact shrinking Ricci solitons. We show that if a compact Ricci soliton $(M,g)$ is a local maximum of Perelman's shrinker entropy, any normalized Ricci flow starting close to it exists for all time ...
Kroencke, Klaus
core   +5 more sources

Some New Characterizations of Trivial Ricci–Bourguignon Solitons

Journal of Mathematics
A Ricci–Bourguignon soliton is a self-similar solution to the Ricci–Bourguignon flow equation, and a Ricci–Bourguignon soliton is called trivial if its potential field is zero or killing.
Hana Al-Sodais, Nasser Bin Turki, Sharief Deshmukh, Bang-Yen Chen, Hemangi Madhusudan Shah   +4 more
doaj   +2 more sources

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, Nasser Bin Turki, Hana Alsodais   +2 more
doaj   +2 more sources

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
openalex   +5 more sources

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
openalex   +6 more sources

Geometric Classifications of Perfect Fluid Space-Time Admit Conformal Ricci-Bourguignon Solitons

Journal of Mathematics
This paper is dedicated to the study of the geometric composition of a perfect fluid space-time with a conformal Ricci-Bourguignon soliton, which is the extended version of the soliton to the Ricci-Bourguignon flow.
Noura Alhouiti, Soumendu Roy, Santu Dey, Fatemah Mofarreh, Akram Ali, Yanlin Li   +5 more
doaj   +2 more sources