We classify Algebraic Ricci Solitons of three-dimensional Lorentzian Lie groups. All algebraic Ricci solitons that we obtain are sol-solitons. In particular, we prove that, contrary to the Riemannian case, Lorentzian Ricci solitons need not to be algebraic Ricci solitons. We classify Algebraic Ricci Solitons of three-d…
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48 results for “Ricci-solitons”
Study on geometric properties of second Ricci solitons.
problem Understanding the geometry of second Ricci solitons.
method Investigation of closed and compact second Ricci soliton manifolds, and immersed submanifolds as well as warped product manifolds.
result Investigation of geometric properties of second Ricci solitons.
This paper provides a study of algebraic Ricci solitons in the pseudo-Riemannian case. In the Riemannian case, all nontrivial homogeneous algebraic Ricci solitons are expanding algebraic Ricci solitons. In this paper, we obtain a steady algebraic Ricci soliton and a shrinking algebraic Ricci soliton in the Lorentzian s…
The paper explores almost Ricci solitons on Finsler spaces, proving conditions for their existence.
problem Characterizing almost Ricci solitons on Finsler measure spaces.
method Introducing and investigating gradient almost Ricci solitons, proving conditions for existence.
result Conditions for the existence of gradient almost Ricci solitons on Finsler measure spaces.
Survey paper analyzes curvature estimates for 4D gradient Ricci solitons.
problem Analyzing curvature estimates for different types of 4D gradient Ricci solitons.
method Comparison and new estimates provided for 4D gradient steady Ricci solitons.
result Sharp curvature estimate for gradient steady Ricci solitons with positive Ricci curvature.
Study characterizes Einstein manifolds in almost Ricci solitons.
problem Characterizing Einstein manifolds in almost Ricci solitons.
method Geometric dynamics and geometric analysis methods.
result Characterizes Einstein manifolds in the class of complete almost Ricci solitons.
Study on pseudo-Riemannian algebraic Ricci solitons in 4D Lie groups.
problem Investigating conditions for pseudo-Riemannian algebraic Ricci solitons on 4D Lie algebras.
method Analyzing the algebraic Ricci soliton equation for each 4D Lie algebra.
result Complete description of pseudo-Riemannian algebraic Ricci solitons in dimension four.
New curvature condition proves rigidity of Bryant Ricci solitons.
problem Proving rigidity of Bryant Ricci solitons.
method Introducing a new curvature-pinching condition and proving rigidity results.
result Rotationally symmetric solutions of steady Ricci solitons are rigid under the new curvature condition.
We introduce the concept {\it -almost Ricci soliton} which extends naturally the {\it almost Ricci soliton} by Pigola-Rigoli-Rimoldi-Setti and show that a compact nontrivial -almost Ricci soliton of dimension no less than three with having defined signal and constant scalar curvature is isometric to a standar…
The study proves triviality and rigidity results for Ricci solitons and estimates their conjugate radius.
problem Understanding the properties and behavior of Ricci solitons.
method Analytical proofs and estimates for various types of Ricci solitons.
result Upper bounds and estimates for conjugate radius of Ricci solitons.
Defines a new metric on Fano Kaehler-Ricci solitons.
problem No specific problem stated; focuses on defining a new metric.
method Defines a Weil-Petersson type metric on the space of shrinking Kaehler-Ricci solitons.
result Proves the independence of the Weil-Petersson metric from choices of Kaehler-Ricci soliton metrics and shows its Kaehler property.
Study on transverse Ricci solitons on compact foliated manifolds.
problem Characterizing transverse Ricci solitons on compact foliated manifolds.
method Investigation of self-similar solutions of the transverse Ricci flow, analysis of taut Riemannian foliations.
result Established relations between taut Riemannian foliations and transverse Ricci solitons, found examples of transverse Ricci solitons.
In this paper, we study Riemannian submersions whose total manifolds admitting a Ricci soliton. Here, we characterize any fiber of such a submersion is Ricci soliton or almost Ricci soliton. Indeed, we obtain necessary conditions for which the target manifold of Riemannian submersion is a Ricci soliton. Moreover, we st…
The paper examines Sasaki-Ricci solitons and their transverse rigidity properties.
problem Understanding the rigidity properties of Sasaki-Ricci solitons as singularity models.
method Established fundamental equations and criteria for transverse rigidity, proving key results about scalar curvature and Weyl tensor.
result Low-dimensional Sasaki-Ricci solitons with constant scalar curvature are Sasaki-Einstein, and those with harmonic Weyl tensor are finite quotients of the sphere.
The purpose of this article is to study implications of a Ricci soliton warped product manifold to its base and fiber manifolds. First, it is proved that if a warped product manifold is Ricci soliton then its factors are Ricci soliton. Then we study Ricci soliton on warped product manifolds admitting either a conformal…
New types of Ricci solitons found in 4D Lorentzian geometry.
problem Understanding Ricci solitons in Lorentzian geometry.
method Analyzing four-dimensional Lie groups for left-invariant Lorentz metrics.
result Any connected and simply connected 4D Lie group admits a left-invariant Lorentz metric that is a Ricci soliton.
In -contact metric manifolds and/or -manifolds, gradient Ricci solitons, compact Ricci solitons and Ricci solitons with pointwise collinear with the structure vector field are studied.
In this paper, we consider -Ricci soliton in the frame-work of Kenmotsu manifolds. First, we prove that if the metric of a Kenmotsu manifold is a -Ricci soliton, then soliton constant is zero. For 3-dimensional case, if admits a -Ricci soliton, then we show that is of constant sectional curvatu…
The paper characterizes Kenmotsu manifolds with conformal η-Ricci solitons.
problem Characterizing Kenmotsu manifolds with conformal η-Ricci solitons.
method Investigating the nature of conformal η-Ricci solitons within the framework of Kenmotsu manifolds.
result An η-Einstein Kenmotsu manifold admitting conformal η-Ricci soliton is an Einstein one.
Study of -Ricci solitons on Kenmotsu 3-manifolds.
problem Exploring -Ricci solitons on Kenmotsu 3-manifolds.
method Examined various types of -Ricci solitons on Kenmotsu 3-manifolds, including those with specific curvature conditions.
result Existence of proper -Ricci solitons on Kenmotsu 3-manifolds.
Paper reviews and proves volume growth estimates for different types of gradient Ricci solitons.
problem Estimating volume growth for gradient Ricci solitons.
method Survey and prove new volume growth estimates.
result New volume growth estimates for expanding gradient Ricci solitons.
Gradient Ricci solitons can be extended to non-gradient Ricci solitons using energy function.
problem Extending the geometry of gradient Ricci solitons to non-gradient Ricci solitons.
method Using energy function to study the geometry.
result A non-steady Ricci soliton with symmetric covariant derivative is gradient.
The concept of the Ricci soliton was introduced by Hamilton. Ricci soliton is defined by vector field and it's a natural generalization of Einstein metric. We have shown earlier that the vector field of Ricci soliton is an infinitesimal harmonic transformation. In our paper, we survey Ricci solitons geometry as an appl…
On the fundamental group of steady gradient Ricci solitons with nonnegative sectional curvaturemath.DG
Paper studies fundamental groups of certain Ricci solitons.
problem Understanding fundamental groups of specific Ricci solitons.
method Analyzes properties of complete steady gradient Ricci solitons with nonnegative sectional curvature.
result Fundamental groups of these solitons are either trivial or infinite.
The paper studies conformal Ricci solitons in warped product spaces.
problem Characterizing conformal Ricci solitons in warped product manifolds.
method Analyzes properties of conformal Ricci solitons in warped product spaces, proving conditions for solitons and characterizing them in terms of vector fields.
result A warped product manifold admitting a conformal Ricci soliton with a concurrent potential vector field is Ricci flat.
Study complete gradient Ricci solitons with zero radial Weyl curvature.
problem Characterize complete gradient Ricci solitons with specific curvature properties.
method Classify complete gradient Ricci solitons with zero radial Weyl curvature for dimensions .
result Completely classified complete gradient Ricci solitons with zero radial Weyl curvature.
A note on the classification of four-dimensional gradient steady and expanding Ricci solitonsmath.DG
Study classifies 4D Ricci solitons with specific curvature conditions.
problem Classifying 4D gradient steady and expanding Ricci solitons with given curvature properties.
method Asymptotically cylindrical and conical assumptions; half-harmonic and half-nonnegative isotropic curvature conditions.
result Partial classification of 4D gradient expanding Ricci solitons with half-nonnegative isotropic curvature.
In this paper we study potential function of gradient steady Ricci solitons. We prove that infimum of potential function decays linearly; in particular, potential function of rectifiable gradient steady Ricci solitons decays linearly. As a consequence, we show that a gradient steady Ricci soliton with bounded potential…
The paper investigates geometrical aspects of static spacetime with almost gradient Ricci solitons.
problem Geometrical properties of static spacetime with almost gradient Ricci solitons.
method Analyzing conditions and properties of static spacetime with almost gradient Ricci solitons.
result Conditions and properties of static spacetime with almost gradient Ricci solitons are determined.
Homogeneous Ricci solitonsmath.DG
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 . In the g…
Paper proves rigidity for Ricci solitons with specific conditions.
problem Understanding the properties of Ricci solitons under various conditions.
method Analyzes shrinking and expanding Ricci solitons with specific constraints.
result Compact shrinking Ricci solitons are Einstein if the potential function is controlled.
This paper classifies Ricci soliton subgroups in a specific type of nilpotent group.
problem Classifying Ricci soliton subgroups in a specific type of nilpotent group.
method Using the properties of nilpotent Iwasawa groups and Lie subgroups.
result Classification of codimension one Lie subgroups of nilpotent Iwasawa groups that are Ricci solitons.
Study Kähler-Ricci solitons on bounded domains, proving they are Kähler-Einstein.
problem Characterize Kähler-Ricci solitons on bounded pseudoconvex domains.
method Prove solitons are Kähler-Einstein under suitable assumptions, using Huang and Xiao's resolution of Cheng's conjecture.
result Kähler-Ricci solitons on bounded pseudoconvex domains are Kähler-Einstein.
The paper explores -conformal -Ricci solitons in Kenmotsu manifolds.
problem Characterizing -conformal -Ricci solitons in Kenmotsu manifolds.
method Analyzing the properties of Kenmotsu metrics and manifolds under -conformal -Ricci solitons.
result Kenmotsu metrics as -conformal -Ricci solitons are Einstein if the soliton vector field is contact.
The study examines 4D steady gradient Ricci solitons with nonnegative curvature away from a compact set.
problem Analyzing noncompact steady gradient Ricci solitons with nonnegative curvature operator.
method Examining the asymptotic behavior of noncompact κ-noncollapsed steady gradient Ricci solitons with nonnegative curvature operator away from a compact set.
result 4D noncompact κ-noncollapsed steady gradient Ricci solitons with nonnegative sectional curvature must be a Bryant Ricci soliton up to scaling.
The paper characterizes Kenmotsu metrics as almost -Ricci solitons.
problem Characterizing Kenmotsu metrics as almost -Ricci solitons.
method Analyzing the geometry of almost contact metrics through -Ricci solitons.
result Kenmotsu metrics are characterized as almost -Ricci solitons under specific conditions.
New expanding Ricci solitons found starting in dimension four.
problem Finding expanding Ricci solitons in specific dimensions.
method Constructing gradient expanding Ricci solitons asymptotic to cones and on trivial vector bundles.
result Continuous families of expanding Ricci solitons on products of Einstein manifolds.
The purpose of this article is to study an -cosymplectic manifold admitting Ricci solitons. Here we consider mainly two classes of Ricci solitons on -cosymplectic manifolds. One is the class of contact Ricci solitons. The other is the class of gradient Ricci solitons, for which we give the local classificatio…
Axisymmetric Ricci solitons are rigid under non-axisymmetric perturbations.
problem Understanding the rigidity of axisymmetric Ricci solitons under perturbations.
method Examined non-axisymmetric perturbations of axisymmetric toric Einstein manifolds and Ricci solitons, establishing a rigidity result.
result Axisymmetric Ricci solitons do not admit constant-angle non-axisymmetric perturbations except for conformally flat cases.
New gradient Ricci solitons found via fiber bundles.
problem Existence of gradient Ricci solitons.
method Warped metrics and fiber bundles.
result Necessary and sufficient conditions for existence.
The paper examines conditions for conformal Ricci solitons on generalized ()-space forms.
problem Conditions for conformal Ricci solitons on generalized ()-space forms.
method Derivation of conditions for solitons to be shrinking, steady, or expanding in terms of conformal pressure p.
result Conditions for a Ricci semi-symmetric generalized ()-space form to form an Einstein manifold when equipped with a conformal Ricci soliton.
The study shows rigidity of Kähler-Ricci solitons on a specific 4D manifold.
problem Investigating the rigidity of Kähler-Ricci solitons near a Kähler model.
method Analyzing gradient shrinking Ricci solitons close to a Kähler model, focusing on norms of the self-dual Weyl tensor and scalar curvature.
result Gradient Ricci solitons on are either half-conformally flat or locally Kähler if certain conditions are met.
The paper characterizes Einstein metrics in Kenmotsu manifolds using specific soliton types.
problem Characterizing Einstein metrics in Kenmotsu manifolds using specific soliton types.
method Proving properties of Kenmotsu metrics as -Ricci solitons and gradient -Ricci solitons.
result Kenmotsu metrics as -Ricci solitons are Einstein if certain conditions are met.
The paper studies Ricci solitons on contact pseudo-metric manifolds and their properties.
problem Characterizing properties of contact pseudo-metric manifolds with Ricci solitons.
method Analyzing specific types of Ricci solitons on Sasakian and contact pseudo-metric manifolds.
result Properties of Ricci solitons on contact pseudo-metric manifolds, leading to Einstein manifolds under certain conditions.
Study 4D steady gradient Ricci solitons reducing to 3D manifolds.
problem Understanding 4D steady gradient Ricci solitons that reduce to 3D.
method Analyzing asymptotic geometry and curvature properties.
result 4D solitons either reduce to spherical space forms or the 3D Bryant soliton.
New classification of gradient steady Ricci solitons with vanishing D-tensor.
problem Classifying gradient steady Ricci solitons with specific properties.
method Extending Cao-Chen's work on Bach-flat gradient Ricci solitons, proving properties for -flat solitons.
result Any -dimensional complete noncompact gradient steady Ricci soliton with vanishing -tensor is either Ricci-flat or isometric to the Bryant soliton.
New classification of 5D nilsolitons using algebraic Ricci soliton equation.
problem Classifying five-dimensional nilsolitons.
method Using algebraic Ricci soliton equation, derived the structure of 7 out of 10 classes of nilmanifolds.
result 7 out of 10 classes of 5D nilmanifolds admit Ricci soliton structure.
Simply-connected shrinking Kähler-Ricci solitons are proven.
problem Simply-connectedness of shrinking Kähler-Ricci solitons.
method Using results by Sun-Zhang and Wylie.
result Shrinking Kähler-Ricci solitons are simply-connected.