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.
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.
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.
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…
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 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.
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.
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 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.
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 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 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. 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. Study of k-almost Yamabe solitons in perfect fluid spacetimes.
problem Analyzing k-almost Yamabe solitons in perfect fluid spacetimes. method Examined perfect fluid spacetimes and k-almost Yamabe solitons using Einstein field equations. result Characterized properties of k-almost Yamabe solitons in perfect fluid 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.
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.
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.
Study of Yamabe solitons on specific geometric manifolds.
problem Characterizing Yamabe solitons on almost contact complex Riemannian manifolds.
method Investigation of two cases: Sasaki-like and torse-forming potentials.
result Explicit examples and theoretical properties confirmed in 3D.
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.
The differential geometry of Kenmotsu manifold is a valuable part of contact geometry with nice applications in other fields such as theoretical physics. In fact, its statistical counterpart, that is, Kenmotsu statistical manifold also has same importance as that of Kenmotsu manifold. Theoretical physicists have also b…
Study on Yamabe solitons on specific complex manifolds, focusing on torse-forming vector fields.
problem Exploring Yamabe solitons on a specific class of complex manifolds.
method Analyzing Yamabe solitons on almost contact complex Riemannian manifolds with a vertical torse-forming vector field.
result Explicit examples of 5-dimensional Lie groups characterized by the study.
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.
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.
The purpose of the paper is to study Yamabe solitons on three-dimensional para-Sasakian, paracosymplectic and para-Kenmotsu manifolds. Mainly, we proved that *If the semi-Riemannian metric of a three-dimensional para-Sasakian manifold is a Yamabe soliton, then it is of constant scalar curvature, and the flow vector fie…
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. Study properties of hyperbolic Yamabe solitons in submanifolds.
problem Characterize and understand hyperbolic Yamabe solitons in submanifolds.
method Define hyperbolic Yamabe flow, prove properties, and classify solitons.
result Prove that hyperbolic Yamabe solitons are pseudosymmetric or metallic shaped.
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 initiate the study of Yamabe and quasi-Yamabe solitons on Euclidean submanifolds whose soliton fields are the tangential components of their position vector fields. Several fundamental results of such solitons were proved. In particular, we classify such Yamabe and quasi-Yamabe solitons on Euclidean hy…
The paper classifies 3D complete gradient Yamabe solitons.
problem Classifying nontrivial 3D complete gradient Yamabe solitons.
method Analyzing properties of Yamabe solitons to show rotationally symmetry.
result Nontrivial non-flat 3D complete steady gradient Yamabe solitons are rotationally symmetric.
Characterizes ∗-k-Ricci-Yamabe solitons on Kenmotsu manifolds.
problem Understanding ∗-k-Ricci-Yamabe solitons on Kenmotsu manifolds. method Analyzes the geometry of ∗-k-Ricci-Yamabe solitons and gradient solitons on Kenmotsu manifolds. result Characterizes the nature of ∗-k-Ricci-Yamabe solitons and gradient solitons. Paper shows constant σk-curvature for quasi k-Yamabe solitons.
problem Understanding constant curvature in quasi k-Yamabe solitons.
method Analyzes conditions for solitons to be gradient and constant curvature.
result Compact quasi k-Yamabe solitons have constant σk-curvature.
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.
Paper shows k-Yamabe solitons have constant curvature under certain conditions.
problem Understanding the properties of k-Yamabe solitons.
method Analyzing the curvature and gradient conditions for k-Yamabe solitons.
result Compact k-Yamabe solitons have constant σk-curvature under certain conditions. The paper classifies expanding gradient Yamabe solitons based on scalar curvature.
problem Classifying expanding gradient Yamabe solitons based on scalar curvature.
method Rigorous analysis of scalar curvature in both cases: greater than and less than the soliton constant.
result Complete classification of nontrivial complete expanding gradient Yamabe solitons.
Study on warped product Yamabe solitons with constant fiber curvature.
problem Characterizing nontrivial warped product Yamabe gradient solitons.
method Investigation of warped product manifolds, derivation of scalar curvature estimates.
result Nontrivial warped product Yamabe gradient solitons have constant scalar curvature in the fiber.
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. Study properties of 3D trans-Sasakian manifolds with η-Yamabe solitons.
problem Properties of 3D trans-Sasakian manifolds with η-Yamabe solitons.
method Investigated curvature conditions and constructed a manifold.
result Construct a 3D trans-Sasakian manifold satisfying η-Yamabe soliton.
The paper characterizes solitons and estimates scalar curvature.
problem Characterizing and estimating scalar curvature of generalized Ricci-Yamabe solitons.
method Characterization and estimation of scalar curvature through soliton properties.
result Conditions for scalar curvature to be constant and estimation of Ricci curvature.
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.
Study CR Yamabe constant, flow, and soliton on CR manifolds.
problem Analyzing CR Yamabe constant, flow, and soliton on CR manifolds.
method Using maximum principles, proving uniqueness for CR Yamabe flow, and studying properties of CR Yamabe soliton.
result Uniqueness theorem for CR Yamabe flow and properties of CR Yamabe soliton.
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. Characterizes gradient Yamabe solitons with specific conditions.
problem Understanding properties of gradient Yamabe solitons.
method Proved conditions leading to constant scalar curvature, subharmonicity, and harmonic potential.
result Gradient Yamabe solitons under certain conditions are of constant scalar curvature.
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.
The study proves rotationally symmetric property of certain shrinking gradient Yamabe solitons.
problem Understanding the rotational symmetry of specific shrinking gradient Yamabe solitons.
method Analyzing nontrivial complete shrinking gradient Yamabe solitons with bounded scalar curvature.
result The assumption of bounded scalar curvature and strict inequality at some point is necessary and sufficient for rotational symmetry.
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.
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 …
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…