The study examines Riemann solitons and almost solitons on specific Kenmotsu manifolds.
problem Characterizing solitons on Kenmotsu manifolds.
method Analysis of Riemann solitons and gradient almost Riemann solitons on almost Kenmotsu manifolds.
result Construction of examples of Kenmotsu and (κ,μ)′-almost Kenmotsu manifolds. The study classifies h-almost Ricci-Yamabe solitons in various paracontact manifolds.
problem Classifying h-almost Ricci-Yamabe solitons in paracontact geometry.
method Characterization and classification of para-Kenmotsu, para-Sasakian, and para-cosymplectic manifolds.
result Characterizations and classifications of various paracontact manifolds.
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.
We prove some results for the solitons of the Ricci-Bourguignon flow, generalizing corresponding results for Ricci solitons. Taking motivation from Ricci almost solitons, we then introduce the notion of Ricci-Bourguignon almost solitons and prove some results about them which generalize previous results for Ricci alm…
Study of almost Yamabe solitons on Kaehler submersions.
problem Characterizing almost Yamabe solitons on Kaehler submersions.
method Analyzing conditions for solitons to be shrinking, steady, or expanding.
result Characterizations for almost Yamabe solitons in terms of extrinsic horizontal scalar curvature.
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.
New examples of solitons found as warped products.
problem Constructing new soliton examples.
method Warped products and explicit descriptions using elementary functions.
result Complete examples of Ricci almost solitons and Ricci-Bourguignon solitons.
In this paper, we completely classify almost Yamabe solitons on hypersurfaces in Euclidean spaces arisen from the position vector field. Some results of almost Yamabe solitons with a concurrent vector field and almost Yamabe solitons on submanifolds in Riemannian manifolds equipped with a concurrent vector field are al…
Study clarifies almost Ricci-Bourguignon solitons and their properties.
problem Understanding the properties of almost Ricci-Bourguignon solitons.
method Revisit and compare with known results of Barros and Ribeiro.
result Identify conditions for compact almost RB-solitons to be trivial or have special properties.
Study on non-gradient Ricci almost solitons in warped products.
problem Understanding non-gradient Ricci almost solitons.
method Construction method and explicit example in warped products.
result Rigidity result for Gaussian soliton.
We introduce the concept {\it h-almost Ricci soliton} which extends naturally the {\it almost Ricci soliton} by Pigola-Rigoli-Rimoldi-Setti and show that a compact nontrivial h-almost Ricci soliton of dimension no less than three with h having defined signal and constant scalar curvature is isometric to a standar…
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.
This paper studies gradient almost Ricci-harmonic soliton with respect to a fixed metric. We rely on analytic techniques to estabilish some basic elliptic and integral equations for the structure of almost Ricci-harmonic soliton which generalizes that of Ricci-hamonic solitons on one hand and that of almost Ricci solit…
Study on solitons in specific geometric manifolds, proving manifold properties and presenting examples.
problem Exploring solitons in almost coKähler and asymptotically harmonic manifolds.
method Analyzing η-Einstein and gradient η-Einstein solitons in various geometric frameworks. result Proves manifold properties and presents examples validating results.
Study on gradient h-almost Yamabe solitons with scalar curvature estimation.
problem Exploring triviality and scalar curvature estimation of gradient h-almost Yamabe solitons.
method Established sufficient conditions for triviality and scalar curvature estimation under integral inequalities involving the scalar curvature and soliton function.
result Extended and refined former works on almost and h-almost Yamabe solitons, characterizing their geometric structures.
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.
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.
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.
In this article we study an almost f-cosymplectic manifold admitting a Ricci soliton. We first prove that there do not exist Ricci solitons on an almost cosymplectic (κ,μ)-manifold. Further, we consider an almost f-cosymplectic manifold admitting a Ricci soliton whose potential vector field is the Reeb vector fie…
The paper studies integral formulas for a specific type of soliton.
problem Integral formulas for compact gradient h-almost Ricci-Bourguignon solitons.
method Investigation of integral formulas and proving properties of solitons.
result Compact, non-trivial h-almost Ricci-Bourguignon solitons are isometric to a Euclidean sphere under certain conditions.
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.
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. The study examines almost Ricci-Yamabe solitons on almost Kenmotsu manifolds and their properties.
problem Characterizing almost Ricci-Yamabe solitons on almost Kenmotsu manifolds.
method Analyzing the conditions for almost Ricci-Yamabe solitons to be η-Einstein and proving local isometry for certain manifolds.
result Properties of almost Ricci-Yamabe solitons on (2n+1)-dimensional (κ,μ)′-AKMs. 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…
The paper introduces and characterizes almost ω-Bach solitons on various product manifolds.
problem Characterizing almost ω-Bach solitons on different manifolds.
method Introducing ω-Bach tensor and defining almost ω-Bach solitons; characterizing them under specific conditions. result Explicitly found gradient almost ω-Bach solitons on specific product manifolds.
Paper examines properties of specific solutions to Yamabe flow.
problem Characterizing quotient almost Yamabe solitons.
method Investigates quotient almost Yamabe solitons and presents conditions for their rigidity.
result Sufficient conditions for quotient almost Yamabe solitons to be trivial or isometric with a sphere.
Paper studies non-gradient almost Yamabe solitons and their properties.
problem Characterizing structures of non-gradient almost Yamabe solitons.
method Investigates conditions for trivial solitons and local warped product structures.
result Almost Yamabe solitons with closed vector fields admit local warped product structures.
The paper characterizes gradient solitons in specific manifold types.
problem Characterizing gradient solitons in almost Kenmotsu manifolds.
method Analyzing (m,ρ)-quasi Einstein solitons within two classes of almost Kenmotsu manifolds. result Characterized gradient (m,ρ)-quasi Einstein solitons in specific manifold types. 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. 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.
Gradient Ricci almost solitons were introduced by Pigola, Rigoli, Rimoldi and Setti. They are defined as solitons except that the metric coefficient is required to be a smooth function rather than a constant. It is shown that any almost soliton is conformal to another almost soliton having a soliton function which is m…
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.
The paper studies a new soliton on Kenmotsu manifolds and derives its scalar curvature.
problem Characterizing a new soliton on Kenmotsu manifolds.
method Analyzing the ∗−κ-Ricci-Bourguignon almost soliton on Kenmotsu structure manifolds. result Derivation of the scalar curvature for a Kenmotsu manifold with the ∗−κ-Ricci-Bourguignon soliton. 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.
Study on solitons in deformed Kenmotsu manifolds with specific vector fields.
problem Analyzing geometric solitons in deformed Kenmotsu manifolds.
method Examined almost Riemann and Ricci solitons in a D-homothetically deformed Kenmotsu manifold with specific vector fields. result Explicitly obtained Ricci and scalar curvatures for some cases, provided a lower bound for Ricci curvature.
Conditions for statistical structures on manifolds derived from solitons.
problem Characterizing statistical structures on manifolds from soliton equations.
method Analyzing gradient solitons on statistical manifolds to derive conditions for statistical structures.
result Established necessary and sufficient conditions for statistical structures under various soliton types.
Study on almost Riemann solitons with gradient or torse-forming vector fields.
problem Characterizing almost Riemann solitons with specific vector fields.
method Using Bochner formula and properties of gradient and torse-forming vector fields.
result Explicit expressions for the soliton function λ under gradient and torse-forming conditions. We consider almost quasi-Yamabe solitons in Riemannian manifolds, derive a Bochner-type formula in the gradient case and prove that under certain assumptions, the manifold is of constant scalar curvature. We also provide necessary and sufficient conditions for a gradient almost quasi-Yamabe soliton on the base manifold…
The paper characterizes specific almost Kenmotsu manifolds with Ricci-Yamabe solitons.
problem Characterizing almost Kenmotsu manifolds with Ricci-Yamabe solitons.
method Analyzing curvature properties and potential vector fields.
result Locally isometric structures of specific almost Kenmotsu manifolds.
Study of generalized almost-Kähler-Ricci solitons and their implications.
problem Existence of first-Chern-Einstein almost-Kähler metrics on compact symplectic Fano manifolds.
method Generalization of Kähler-Ricci solitons to almost-Kähler setting, study of moment map and Lie algebra of holomorphic vector fields.
result Existence of generalized almost-Kähler-Ricci solitons as obstructions and implications for symplectic Fano manifolds.
New volume comparison theorem for gradient Ricci almost solitons.
problem Volume comparison and rigidity of gradient Ricci almost solitons.
method Established a new volume comparison theorem with Bakry-Emery Ricci curvature.
result New volume rigidity result for gradient Ricci almost solitons.
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 characterizes a class of almost Kenmotsu manifolds with quasi Yamabe solitons.
problem Characterizing almost Kenmotsu manifolds with quasi Yamabe solitons.
method Analyzing the properties of quasi Yamabe solitons on (k,μ)′-almost Kenmotsu manifolds. result If a (k,μ)′-almost Kenmotsu manifold admits a quasi Yamabe soliton, then V is a constant multiple of ξ, V is a strict infinitesimal contact transformation, and (£Vh′)X=0 for any vector field X. Study properties of specific solitons on submanifolds with special vector fields.
problem Characterize almost η-Ricci and Yamabe solitons on submanifolds. method Analyze submanifolds isometrically immersed into Riemannian manifolds with specific potential vector fields.
result Necessary and sufficient conditions for hypersurfaces in the unit sphere to be solitons.
The study examines gradient almost Yamabe solitons in warped product manifolds and their geometric properties.
problem Investigating the geometry of gradient almost Yamabe solitons in warped product manifolds.
method Presenting geometric rigidity results, investigating existence conditions, and classifying specific solitons.
result Classification of rotational gradient almost Yamabe solitons in RimesfRn. 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 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 \(ξ(σ)=0\).
Study on a new type of solitons on specific geometric manifolds.
problem Characterizing new types of solitons in geometric structures.
method Generalization of Ricci-like solitons with specific properties and conditions.
result Conditions for these solitons to be equivalent to almost Einstein-like metrics.