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.
The paper examines conditions for conformal Ricci solitons on generalized (κ,μ)-space forms.
problem Conditions for conformal Ricci solitons on generalized (κ,μ)-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 (κ,μ)-space form to form an Einstein manifold when equipped with a conformal Ricci soliton. 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 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 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 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 explores ∗-conformal η-Ricci solitons in Kenmotsu manifolds.
problem Characterizing ∗-conformal η-Ricci solitons in Kenmotsu manifolds. method Analyzing the properties of Kenmotsu metrics and manifolds under ∗-conformal η-Ricci solitons. result Kenmotsu metrics as ∗-conformal η-Ricci solitons are Einstein if the soliton vector field is contact. The paper classifies conformal solitons in pseudo-Euclidean spaces.
problem Classifying conformal solitons in pseudo-Euclidean spaces.
method Classification through pseudo-Riemannian hypersurfaces and position vector fields.
result Complete classification of conformal solitons in pseudo-Euclidean spaces.
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.
The paper characterizes Clairaut conformal submersions on Ricci solitons.
problem Characterizing Clairaut conformal submersions on Ricci solitons.
method Calculating scalar and Ricci tensors, providing necessary conditions for fibres and base manifolds to be Ricci solitons and Einstein, and solving Poisson equations.
result Necessary and sufficient conditions for Clairaut conformal submersions to be harmonic.
Study on Yamabe solitons with applications and structure elucidation.
problem Understanding the structure of Yamabe solitons and their applications.
method Investigation of complete gradient conformal solitons under specific conditions.
result Affirmative partial answer to Yamabe soliton conjecture.
In this paper we study *-Conformal η-Ricci soliton on Sasakian manifolds. Here, we discuss some curvature properties on Sasakian manifold admitting *-Conformal η-Ricci soliton. We obtain some significant results on *-Conformal η-Ricci soliton in Sasakian manifolds satisfying R(ξ,X).S = 0, S(ξ,X).R = 0, {\overline}P(ξ,X…
In this paper, we classify n-dimensional (n>2) complete noncompact locally conformally flat gradient steady solitons. In particular, we prove that a complete noncompact non-flat conformally flat gradient steady Ricci soliton is, up to scaling, the Bryant soliton.
Characterizes potential function of almost conformal Ricci solitons on Sasakian manifolds.
problem Characterizing potential functions of almost conformal Ricci solitons on Sasakian manifolds.
method Characterization through the potential function f and non-dynamical scalar field p. result Established a sufficient condition for an almost conformal Ricci soliton to be an almost conformal gradient Ricci soliton.
The paper explores conformal submersions from Ricci solitons to Riemannian manifolds.
problem Characterizing conformal submersions from Ricci solitons.
method Analyzing properties of the O'Neill tensor, calculating Ricci tensors, and finding necessary conditions for harmonic maps.
result Necessary conditions for fibers and base manifold to be Ricci solitons, almost Ricci solitons, and Einstein.
Local gradient estimates for eigenfunctions on conformal solitons improve Liouville theorems.
problem Estimating eigenfunctions on conformal solitons.
method Proving local gradient estimates for positive eigenfunctions of L-operator. result Improved Liouville theorems for Lu=0 on conformal solitons. 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. 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 geometric structures in perfect fluid spacetimes with specific metrics.
problem Analyzing the geometric properties of perfect fluid spacetimes with specific metrics.
method Investigates conditions for conformal Ricci-Yamabe soliton and derives Laplace equations.
result Conditions for expanding, steady, or shrinking conformal Ricci-Yamabe solitons are identified.
In this paper we extend some well-known rigidity results for conformal changes of Einstein metrics to the class of generalized quasi-Einstein (GQE) metrics, which includes gradient Ricci solitons. In order to do so, we introduce the notions of conformal diffeomorphisms and vector fields that preserve a GQE structure. W…
In this note we prove that any four-dimensional half conformally flat gradient steady Ricci soliton must be either Bryant's soliton or Ricci flat. We also classify four-dimensional half conformally flat gradient shrinking Ricci solitons with bounded curvature.
The paper studies special solitons on Riemannian manifolds with specific vector fields.
problem Characterizing conformal and ∗-Yamabe solitons with torse forming potential vector fields. method Analyzing solitons under different connections (Riemannian, semi-symmetric, projective semi-symmetric) and developing examples.
result Characterizations and properties of conformal and ∗-Yamabe solitons with torse forming vector fields. The study classifies gradient Ricci solitons with specific vector fields.
problem Characterizing gradient Ricci solitons with closed conformal vector fields.
method Analyzing properties of gradient Ricci solitons with constant scalar curvature and closed conformal vector fields.
result Gradient Ricci solitons with these properties are isometric to specific spaces.
We provide the classification of locally conformally flat gradient Yamabe solitons with positive sectional curvature. We first show that locally conformally flat gradient Yamabe solitons with positive sectional curvature have to be rotationally symmetric and then give the classification and asymptotic behavior of all r…
The local structure of half conformally flat gradient Ricci almost solitons is investigated, showing that they are locally conformally flat in a neighborhood of any point where the gradient of the potential function is non-null. In opposition, if the gradient of the potential function is null, then the soliton is a ste…
In this paper, we first apply an integral identity on Ricci solitons to prove that closed locally conformally flat gradient Ricci solitons are of constant sectional curvature. We then generalize this integral identity to complete noncompact gradient shrinking Ricci solitons, under the conditions that the Ricci curvatur…
This paper classifies solitons under specific tensor conditions.
problem Classifying solitons under vanishing conditions on the Weyl, Cotton, and Cao-Chen tensors.
method Analyzing complete conformal gradient solitons and using tensor conditions.
result Classification of complete nontrivial locally conformally flat conformal gradient solitons.
We show that any locally conformally flat ancient solution to the Ricci flow must be rotationally symmetric. As a by-product, we prove that any locally conformally flat Ricci soliton is a gradient soliton in the shrinking and steady cases as well as in the expanding case, provided the soliton has nonnegative curvature.
Conditions for Riemannian manifolds to be Euclidean spheres or spaces.
problem Characterizing Riemannian manifolds with specific vector fields.
method Analyzing conformal Killing vector fields and Ricci solitons.
result Conditions for nontrivial closed affine conformal Killing vector fields.
We construct examples of Bach-flat gradient Ricci solitons which are neither half conformally flat nor conformally Einstein.
The paper classifies invariant gradient k-Yamabe solitons in pseudo-Euclidean spaces.
problem Characterizing invariant gradient k-Yamabe solitons in pseudo-Euclidean spaces. method Characterization through the action of an (n−1)-dimensional translation group and classification of rotational invariant solutions. result Infinitely many explicit examples of geodesically complete steady gradient k-Yamabe solitons are constructed. The paper investigates Ricci almost solitons linked to conformal vector fields.
problem Investigating Ricci almost solitons on manifolds.
method Analyzing semi-Riemannian manifolds and conformal vector fields.
result Connected totally umbilic manifolds inherit Ricci almost soliton structures via conformal vector fields.
Study on Ricci-Bourguignon solitons on specific product spaces.
problem Characterizing Ricci-Bourguignon solitons on sequential warped products.
method Obtained necessary conditions for solitons to be Einstein manifolds under specific potential fields.
result Conditions for Ricci-Bourguignon solitons to be Einstein are identified.
We consider four dimensional conformally flat homogeneous pseudo Riemannian manifolds. According to forms (Seger types) of the Ricci operator, we provide a full classification of four dimensional pseudo Riemannian conformally flat homogeneous Ricci solitons.
In this paper we show that all conformal metrics to a pseudo-euclidean space invariant under the translation group, and all the conformal metrics product manifold also invariant by translation where F m it is Ricci flat semi-Riemannian manifold, are gradient Ricci almost soliton. We also proved that all conformal metri…
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.
In this paper we introduce, in the Riemannian setting, the notion of conformal Ricci soliton, which includes as particular cases Einstein manifolds, conformal Einstein manifolds and (generic and gradient) Ricci solitons. We provide here some necessary integrability conditions for the existence of these structures that …
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 paper classifies solitons for mean curvature flow in hyperbolic space.
problem Mean curvature flow in hyperbolic space.
method Study of conformal solitons in the upper half-space model of hyperbolic space.
result Classification of cylindrical and rotationally symmetric examples, including grim-reaper cylinders and bowl/winglike solitons.
Yamabe solitons defined on specific Sasaki-like manifolds.
problem Defining Yamabe solitons on Sasaki-like almost contact B-metric manifolds.
method Contact conformal transformation of manifold components to define Yamabe solitons.
result Explicit 5-dimensional Lie group example of a Yamabe soliton.
It is shown that locally conformally flat Lorentzian gradient Ricci solitons are locally isometric to a Robertson-Walker warped product, if the gradient of the potential function is non null, and to a plane wave, if the gradient of the potential function is null. The latter gradient Ricci solitons are necessarily stead…
Study inverse curve shortening flow on hyperbolic plane, classifying solitons.
problem Understanding the behavior of curves in hyperbolic geometry under a specific flow.
method Classifying solitons with respect to vector fields and studying their properties.
result Parabolic solitons are graphs on the y-axis, conformal solitons on the x-axis.
The paper proves rigidity of certain solitons with specific properties.
problem Classifying and understanding Bach-flat gradient Schouten solitons.
method Analyzing the properties of Schouten solitons and their Ricci tensors.
result Rigidity of certain Schouten solitons under specific conditions.
In this paper we prove that any complete conformal gradient soliton with nonnegative Ricci tensor is either isometric to a direct product R×Nn−1, or globally conformally equivalent to the Euclidean space Rn or to the round sphere Sn. In particular, we show that any comple…
We describe the local structure of self-dual gradient Ricci solitons in neutral signature. If the Ricci soliton is non-isotropic then it is locally conformally flat and locally isometric to a warped product of the form I×φN(c), where N(c) is a space of constant curvature. If the Ricci soliton is isotro…
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 S2imesR2 are either half-conformally flat or locally Kähler if certain conditions are met. The paper classifies a type of solitons in Euclidean spaces.
problem Classifying generalized Yamabe solitons on hypersurfaces.
method Completely classified solitons arising from the position vector field.
result Classification of generalized Yamabe solitons on hypersurfaces in Euclidean spaces.
The paper examines conditions for a vector field to be Killing in almost Yamabe solitons.
problem Conditions for a vector field to be Killing in almost Yamabe solitons.
method Investigation of almost Yamabe solitons on compact and non-compact manifolds.
result Sufficient conditions for the defining conformal vector field to be Killing.