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.
The paper studies special solitons on specific contact metric manifolds.
problem Characterizing solitons on N(k)-contact metric manifolds.
method Analyzing ∗-conformal Einstein solitons and gradient solitons on N(k)-contact metric manifolds. result Conditions for solitons to be expanding, steady, or shrinking are determined.
Study properties of Kenmotsu manifolds with conformal η-Einstein soliton metrics.
problem Properties of Kenmotsu manifolds with specific soliton metrics.
method Investigated properties and constructed a 3D example.
result Properties and construction of 3D Kenmotsu manifold with conformal η-Einstein soliton.
Study on Ricci-like solitons and gradient solitons on specific manifolds.
problem Characterizing solitons on Sasaki-like almost contact B-metric manifolds.
method Introduced and studied Ricci-like solitons with arbitrary potential and gradient solitons. Proved properties of the Ricci tensor and soliton coefficients.
result Gradient almost Ricci-like solitons have constant soliton coefficients.
Study of solitons in a specific type of contact metric manifold.
problem Characterizing solitons in (α,β)-contact metric manifolds. method Analyzing almost Riemann and Ricci solitons under Ricci symmetry conditions.
result Characterization of solitons in (α,β)-contact metric manifolds. The paper studies ∗-η-Ricci-Yamabe solitons on α-Cosymplectic manifolds.
problem Exploring ∗-η-Ricci-Yamabe solitons on α-Cosymplectic manifolds. method Analyzing curvature properties and developing soliton characteristics with respect to quarter-symmetric metric connection.
result Characteristics and nature of ∗-η-Ricci-Yamabe solitons on α-Cosymplectic manifolds. Study on para-Sasakian metrics and their solitons.
problem Characterizing para-Sasakian metrics with conformal η-Ricci solitons.
method Analyzing the properties of para-Sasakian metrics under conformal η-Ricci solitons.
result Para-Sasakian metrics admitting conformal η-Ricci solitons are η-Einstein.
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 η-Ricci solitons and gradient η-Ricci solitons. result Kenmotsu metrics as η-Ricci solitons are Einstein if certain conditions are met. In this paper, we investigate the relationship between algebraic soliton metrics and soliton metrics for geometric evolution equations on Lie groups. After discussing the general relationship between algebraic soliton metrics and soliton metrics, we investigate the cross curvature flow and the second order renormalizat…
We investigate Kähler metrics conformal to gradient Ricci solitons, and base metrics of warped product gradient Ricci solitons. The latter we name quasi-solitons. A main assumption that is employed is functional dependence of the soliton potential, with the conformal factor in the first case, and with the warping funct…
The paper studies η−Ricci solitons on contact pseudo-metric manifolds and their properties.
problem Characterizing properties of contact pseudo-metric manifolds with η−Ricci solitons. method Analyzing specific types of η−Ricci solitons on Sasakian and K−contact pseudo-metric manifolds. result Properties of η−Ricci solitons on contact pseudo-metric manifolds, leading to η−Einstein manifolds under certain conditions. 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. This paper connects soliton-type metrics with weighted CSCK metrics on Fano manifolds.
problem Existence and properties of weighted constant scalar curvature Kähler metrics.
method Introducing a weight function g(v,w) and proving equivalence between (v,w)-CSCK metrics and g(v,w)-solitons. result Existence of (v,w)-CSCK metrics in the first Chern class is equivalent to existence of g(v,w)-solitons. Fano varieties get Mabuchi solitons if they have extremal Kähler metrics.
problem Characterizing Fano varieties with Mabuchi solitons.
method Using Yau-Tian-Donaldson type correspondence for v-solitons.
result Existence of Mabuchi solitons linked to existence of extremal Kähler metrics.
New families of Ricci solitons found with collapsing volume.
problem Finding new Ricci solitons with specific volume behavior.
method Reduced soliton equation to Monge-Ampère equation coupled with ODEs.
result Explicit complete expanding solitons and existence results for other types.
Article establishes criteria for multiplier Hermitian-Einstein metrics on KSM-manifolds.
problem Existence of multiplier Hermitian-Einstein metrics on Fano manifolds.
method Criterion based on KSM-data and continuous paths connecting solitons.
result Explicit example of a KSM-manifold with a family of multiplier Hermitian-Einstein metrics.
The study investigates properties of a specific Riemannian manifold with a semi-symmetric non-metric connection.
problem Characterizing properties of a Riemannian manifold with a semi-symmetric non-metric connection.
method Construction of a non-trivial example, proving manifold properties based on the metric being a gradient soliton or Yamabe soliton.
result A manifold with a semi-symmetric non-metric connection and gradient Ricci/Yamabe soliton is of constant curvature.
Study new Einstein-like metrics and their properties.
problem Characterize a new class of quasi-Einstein metrics.
method Investigate modified Ricci solitons and their relationships.
result Prove rigidity of standard spheres under specific conditions.
In N(k)-contact metric manifolds and/or (k,μ)-manifolds, gradient Ricci solitons, compact Ricci solitons and Ricci solitons with V pointwise collinear with the structure vector field ξ are studied.
In this paper, we use less topological restrictions and more geometric and analytic conditions to obtain some sufficient conditions on Yamabe solitons such that their metrics are Yamabe metrics, that is, metrics of constant scalar curvature. More precisely, we use properties of conformal vector fields to find several s…
The study of quasi Yamabe solitons on 3D contact metric manifolds with specific curvature condition.
problem Investigating quasi Yamabe solitons on 3D contact metric manifolds with a specific curvature condition.
method Analyzing the properties of quasi Yamabe solitons on 3D contact metric manifolds with Qφ = φQ and proving the conditions under which the soliton vector field is constant, the scalar curvature is constant, and the manifold is Sasakian.
result If a 3D contact metric manifold M with Qφ = φQ admits a quasi Yamabe soliton with a non-zero soliton vector field V collinear with the Reeb vector field ξ, then V is a constant multiple of ξ, the scalar curvature is constant, and the manifold is Sasakian.
The study explores δ-almost gradient Yamabe solitons on pseudo-Riemannian manifolds.
problem Characterizing δ-almost gradient Yamabe solitons on pseudo-Riemannian manifolds.
method Analyzing δ-almost Yamabe solitons within the framework of para-contact metric manifolds, proving properties and conditions for solitons.
result Characterization of δ-almost gradient Yamabe solitons on K-paracontact metric manifolds.
We show that a left-invariant metric g on a nilpotent Lie group N is a soliton metric if and only if a matrix U and vector v associated the manifold (N,g) satisfy the matrix equation Uv = [1], where [1] is a vector with every entry a one. We associate a generalized Cartan matrix to the matrix U and use the theory of Ka…
The study explores rigid constraints on almost Ricci-Bourguignon solitons on contact metric three-manifolds.
problem Investigating constraints on almost Ricci-Bourguignon solitons on contact metric three-manifolds.
method Using a local orthonormal \(\varphi\)-basis, derived the full component form of the almost Ricci-Bourguignon soliton equation.
result For contact metric three-manifolds satisfying \(Qξ=σξ\), a collinear potential field must vanish on the non-Sasakian region whenever \(ξ(σ)=0\).
The paper characterizes contact metric manifolds with specific solitons.
problem Characterizing contact metric manifolds with ∗-conformal Ricci solitons. method Analyzing properties of (2n+1)-dimensional N(k)-contact metric manifolds. result The manifold is locally isometric to a flat (n+1)-dimensional manifold and an n-dimensional manifold of constant curvature 4. Unique Kähler-Ricci solitons found for S^1-invariant metrics.
problem Existence and uniqueness of Kähler-Ricci solitons.
method Momentum construction for S^1-invariant Kähler metrics.
result These solitons are unique in their Kähler class.
New solitons defined for Sasaki-like almost contact complex Riemannian manifolds.
problem Characterizing new solitons in Sasaki-like almost contact complex Riemannian manifolds.
method Defined β-Ricci-Bourguignon-like almost solitons with special potential. result Characterized geometrically and constructed examples of new solitons.
Proves triviality and nonexistence of gradient Ricci solitons as warped metrics.
problem Proving triviality and nonexistence of gradient Ricci solitons as warped metrics.
method Proved through the construction of gradient Ricci solitons as warped products and studying Ricci-Hessian type manifolds.
result Gradient Ricci solitons are trivial and non-existent as warped metrics.
In this paper we consider connections between Ricci solitons and Einstein metrics on homogeneous spaces. We show that a semi-algebraic Ricci soliton admits an Einstein one-dimensional extension if the soliton derivation can be chosen to be normal. Using our previous work on warped product Einstein metrics, we show that…
The study classifies contact metric manifolds based on Ricci-Yamabe solitons.
problem Classifying contact metric manifolds based on Ricci-Yamabe solitons.
method Analyzing specific types of solitons in contact metric manifolds.
result Contact metric manifolds are classified based on the properties of Ricci-Yamabe solitons.
Survey on Kähler-Einstein and weighted solitons on Fano manifolds.
problem Existence of coupled Kähler-Einstein metrics and weighted solitons on Fano manifolds.
method Generalization of algebraic conditions for K-polystability.
result Existence of coupled Kähler-Einstein metrics and weighted solitons is equivalent to algebraic conditions.
This paper studies Kähler-Ricci solitons on Heisenberg groups and related metrics.
problem Investigating Kähler-Ricci solitons on Heisenberg groups and related metrics.
method Developed an ansatz for Kähler metrics, specialized to frame-dependent PDEs for gradient Kähler-Ricci solitons, and examined curvature properties and asymptotics.
result Found complete expanding gradient Kähler-Ricci solitons under the action of the (2m-1)-dimensional Heisenberg group.
Study identifies Kähler-Einstein, Kähler-Ricci soliton, and Sasaki-Einstein metrics on log del Pezzo surfaces.
problem Characterizing log del Pezzo surfaces with specific geometric properties.
method Examining two classes of non-toric log del Pezzo surfaces and analyzing their geometric properties.
result Examples found that admit Kähler-Ricci solitons but not Sasaki-Einstein cone links.
The object of this paper is to study η-Ricci solitons on (ε)-almost paracontact metric manifolds. We investigate η-Ricci solitons in the case when its potential vector field is exactly the characteristic vector field ξ of the (ε)-almost paracontact metric manifold and when the potential ve…
The paper shows how to stabilize perturbed Kähler-Ricci solitons.
problem Stabilizing perturbed Kähler-Ricci solitons.
method Normalized Kähler-Ricci flow starting from perturbed metrics.
result The flow converges to an asymptotically conical gradient expanding Kähler-Ricci soliton.
The two-loop renormalization group flow is studied via the induced bracket flow on 3D unimodular Lie groups. A number of steady solitons are found. Some of these steady solitons come from maximally symmetric metrics that are steady, shrinking, or expanding solitons under Ricci flow, while others are not obviously relat…
Smooth approximations of Kähler-Ricci solitons found using quantized metrics and Futaki invariants.
problem Finding smooth approximations of Kähler-Ricci solitons on Fano manifolds.
method Using semiclassical estimates and quantized Futaki invariants to extend a strategy from Donaldson and Tian-Zhu.
result Smooth approximations of Kähler-Ricci solitons can be found as quantized metrics.
We present a general numerical method for investigating prescribed Ricci curvature problems on toric Kähler manifolds. This method is applied to two generalisations of Einstein metrics, namely Ricci solitons and quasi-Einstein metrics. We begin by recovering the Koiso--Cao soliton and the Lü--Page--Pope quasi-Einstein …
Study on Ricci solitons on tangent and unit tangent bundles.
problem Characterizing Ricci solitons on tangent and unit tangent bundles.
method Analyzing pseudo-Riemannian g-natural metrics and their Ricci soliton properties. result Classification of conformal vector fields and existence of non-Einstein Ricci solitons.
The paper studies how certain solitons on Fano manifolds extend to nearby deformations.
problem Conditions for weighted solitons to extend to nearby deformations of Fano manifolds.
method Analyzes the Kuranishi family of Fano manifolds and uses equivariant automorphism groups.
result All members of the Kuranishi family of a Fano manifold with a weighted soliton have weighted solitons if and only if the dimensions of their T-equivariant automorphism groups are equal to that of the original manifold.
The article investigates almost Riemann solitons and gradient almost Riemann solitons in a specific type of manifold.
problem Investigating almost Riemann solitons and gradient almost Riemann solitons in a non-cosymplectic normal almost contact metric manifold.
method Analyzing properties of the manifold and its metrics under specific conditions.
result Established conditions under which almost Riemann solitons and gradient almost Riemann solitons reduce to known types of solitons or have specific properties.
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.
The aim of this article is to study the k-almost Ricci soliton and k-almost gradient Ricci soliton on contact metric manifold. First, we prove that if a compact K-contact metric is a k-almost gradient Ricci soliton then it is isometric to a unit sphere S2n+1. Next, we extend this result on a compact k-almost Ricci soli…
Study properties of para-Kähler manifolds with conformal Einstein soliton metrics.
problem Properties of para-Kähler manifolds with conformal Einstein soliton metrics.
method Investigated curvature properties of para-Kähler manifolds admitting conformal Einstein soliton.
result Certain curvature properties of para-Kähler manifolds were studied.
The paper classifies geometric structures of δ-almost Yamabe solitons on paracontact metric manifolds.
problem Characterizing δ-almost Yamabe solitons on paracontact metric manifolds.
method Investigation of geometric structures under specific assumptions, including quarter-symmetric non-metric connections.
result Conditions for δ-almost Yamabe solitons to be expanding, steady, or shrinking.
Exposes new connections between weighted Kähler-Ricci solitons and Ricci-flat Kähler cone metrics.
problem Exploring connections between weighted Kähler-Ricci solitons and Ricci-flat Kähler cone metrics.
method Surveying and reviewing recent works, transforming complex Monge-Ampère equations, and proving the YTD conjecture.
result Established a transformation from irregular Sasaki-Einstein metrics to g-solitons on quasi-regular quotients. Researchers prove isoperimetric inequality in specific steady Ricci solitons.
problem Proving the isoperimetric inequality in steady Ricci solitons.
method Utilized Guan-Li-Wang's result on warped product metrics and analyzed the soliton structure.
result Proved the isoperimetric inequality in the cigar and Bryant steady solitons.
Study shows expanding Ricci solitons from specific metric cones.
problem Analyzing Ricci flows from weakly PIC1 metric cones.
method Complete weakly PIC1 Ricci flows with Euclidean volume growth.
result Ricci flows must be expanding gradient Ricci solitons.