Study on gradient solitons in warped product manifolds.
problem Characterizing gradient solitons in warped product manifolds.
method Derive a Bochner-type formula and prove conditions for solitons.
result Warped product manifolds with gradient solitons have constant scalar curvature.
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 on Yamabe and quasi-Yamabe solitons on Euclidean submanifolds.
problem Characterizing solitons on Euclidean submanifolds.
method Investigation of solitons with tangential components of position vector fields.
result Classification of Yamabe and quasi-Yamabe solitons on Euclidean hypersurfaces.
The study characterizes quasi Yamabe solitons with potential vector fields.
problem Characterizing quasi Yamabe solitons with specific properties.
method Analyzing potential vector fields and their norms in quasi Yamabe solitons.
result If the potential vector field has a finite global norm in a complete non-trivial, non-compact quasi Yamabe soliton with finite volume, the scalar curvature becomes constant and the soliton reduces to a Yamabe soliton.
We prove that a nontrivial complete generalized quasi Yamabe gradient soliton (M; g) must be a quasi Yamabe gradient soliton on each connected component of M and that a nontrivial complete locally conformally at generalized quasi Yamabe gradient soliton has a special warped product structure.
The study classifies specific types of solitons with bounded scalar curvature.
problem Classifying quasi-Yamabe gradient solitons with bounded scalar curvature.
method Analyzing complete, nontrivial solitons with scalar curvature bounded above or below.
result Classification of specific types of solitons with bounded scalar curvature.
In this paper, we introduce the concept of quasi Yamabe gradient solitons, which generalizes the concept of Yamabe gradient solitons. By using some ideas in [7,8], we prove that n-dimensional (n≥3) complete quasi Yamabe gradient solitons with vanishing Weyl curvature tensor and positive sectional curvature must …
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.
Study on solitons in Kenmotsu statistical manifolds and submanifolds.
problem Investigating solitons in Kenmotsu statistical manifolds and their submanifolds.
method Examined statistical solitons and Yamabe solitons, studied curvature properties, and analyzed submanifolds with concircular and concurrent vector fields.
result Discussed the behavior of almost quasi-Yamabe solitons on submanifolds of Kenmotsu statistical manifolds.
Study on gradient solitons on specific manifolds.
problem Existence and properties of gradient solitons on warped product manifolds.
method Analyzing necessary and sufficient conditions for the existence of generalized quasi Yamabe gradient solitons.
result Existence of non-trivial gradient Yamabe solitons on specific spacetimes.
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.
In this note we prove that a (anti-)self dual quasi Yamabe soliton with positive sectional curvature is rotationally symmetric. This generalizes a recent result of G. Huang and H. Li in dimension four. Whence, (anti-) self dual gradient Yamabe solitons with positive sectional curvature is rotationally symmetric. We als…
This paper classifies Kähler manifolds with specific Einstein-type properties.
problem Classifying gradient Einstein-type Kähler manifolds with α=0. method Unified framework of Einstein-type manifolds, focusing on classification with α=0. result Complete classification of non-trivial, complete gradient Einstein-type Kähler manifolds with α=0. Study on η-Ricci-Yamabe solitons on Riemannian submersions.
problem Characterizing η-Ricci-Yamabe solitons on Riemannian submersions. method Analyzing conditions for η-Ricci-Yamabe solitons on submersions and deriving Laplacian equations. result Classification of fiber and target manifolds as η-Ricci-Yamabe solitons under various conditions. 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.
Study on Ricci-Bourguignon solitons and almost solitons, generalizing previous results.
problem Analyzing solitons and almost solitons in the context of Ricci-Bourguignon flow.
method Generalizing results for Ricci solitons and introducing Ricci-Bourguignon almost solitons, proving results and deriving integral formulas.
result Compact gradient Ricci-Bourguignon almost solitons with constant scalar curvature or conformal associated vector field are isometric to Euclidean spheres.
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.
Study k-almost Ricci solitons on contact metric manifolds.
problem Characterize k-almost Ricci solitons on contact metric manifolds.
method Prove isometric properties and extend results for k-almost gradient Ricci solitons and k-almost Ricci solitons.
result Compact K-contact metric manifolds that are k-almost gradient Ricci solitons are isometric to a unit sphere.
The paper classifies almost Yamabe solitons on hypersurfaces and submanifolds in Euclidean spaces.
problem Classifying almost Yamabe solitons on various geometric structures.
method Analyzing hypersurfaces and submanifolds with position and concurrent vector fields.
result Complete classification of almost Yamabe solitons on hypersurfaces and submanifolds.
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.
The study examines Ricci solitons in specific types of manifolds.
problem Investigating Ricci solitons in almost f-cosymplectic manifolds. method Analyzing properties of almost f-cosymplectic manifolds and proving theorems about the existence and classification of Ricci solitons. result Classification of three-dimensional η-Einstein almost f-cosymplectic manifolds admitting Ricci solitons. 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.
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.
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.
Paper studies equations for a type of soliton with applications.
problem Analyzing a specific type of soliton structure.
method Analytic techniques to establish elliptic and integral equations.
result Established basic structural equations for almost Ricci-harmonic solitons.
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…
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.
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.
No Ricci solitons found in almost Kenmotsu manifolds.
problem Existence of Ricci solitons in almost Kenmotsu manifolds.
method Analyzing the Reeb potential vector field in AKM. result No Ricci solitons exist in almost Kenmotsu manifolds.
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 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.
Study bounds Ricci curvature in (LCS)n-manifolds with almost η-Ricci solitons.
problem Bounding Ricci curvature in (LCS)n-manifolds with specific solitons. method Provided lower and upper bounds for Ricci curvature, derived a Bochner-type formula.
result Derived bounds and consequences for (LCS)n-manifolds with almost η-Ricci solitons. 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.
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.
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…