Study Ricci vector fields on 2D space with diagonal metrics.
problem Understanding Ricci vector fields on 2D space with specific metrics.
method Examined Ricci vector fields on R2 with a diagonal metric. result Characterized Ricci vector fields on R2 with a diagonal metric. 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. A Ricci soliton (M,g,v,λ) on a Riemannian manifold (M,g) is said to have concurrent potential field if its potential field v is a concurrent vector field. Ricci solitons arisen from concurrent vector fields on Riemannian manifolds were studied recently in \cite{CD2}. The most important concurrent vector field is …
Study on mixed Killing vector fields on Cigar Ricci-Bourguignon solitons.
problem Characterizing mixed Killing vector fields on Cigar Ricci-Bourguignon solitons.
method Analyzing the condition LVLVg=fLVg and using rigidity phenomena. result Dimension of complete mixed Killing fields is 5 and a basis is explicitly determined.
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.
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.
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.
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. In this paper, we consider ∗-Ricci soliton in the frame-work of Kenmotsu manifolds. First, we prove that if the metric of a Kenmotsu manifold M is a ∗-Ricci soliton, then soliton constant λ is zero. For 3-dimensional case, if M admits a ∗-Ricci soliton, then we show that M is of constant sectional curvatu…
Study vector fields on hyperbolic spaces to create Ricci-Bourguignon solitons.
problem Characterize vector fields on hyperbolic spaces Hn that transform them into Ricci-Bourguignon solitons. method Detailed geometric study of vector fields in dimensions n=2,3 and n≥3, focusing on dual forms in odd dimensions. result Dual forms of these vectors are contact forms in odd dimensions.
A Ricci soliton (Mn,g,v,λ) on a Riemannian manifold (Mn,g) is said to have concurrent potential field if its potential field v is a concurrent vector field. In the first part of this paper we completely classify Ricci solitons with concurrent potential fields. In the second part we derive a necessary and suffic…
Study on dimensions of Killing vector fields on gradient Ricci solitons.
problem Estimating dimensions of Killing vector fields on gradient Ricci solitons.
method Analyzes the structure of gradient Ricci solitons to estimate dimensions of Killing vector fields.
result Maximal dimension of Killing vector fields on irreducible non-trivial gradient Ricci solitons.
In this paper geometrical aspects of perfect fluid spacetime with torse-forming vector field ξare discribed and Ricci soliton in perfect fluid spacetime with torse-forming vector field ξare determined. Conditions for the Ricci soliton to be expanding, steady or shrinking are also given.
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.
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.
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 classifies Ricci solitons and studies harmonic vector fields on a specific Thurston geometry.
problem Classifying Ricci solitons and studying harmonic vector fields in a specific Thurston geometry.
method Left-invariant Riemannian metric classification and analysis of harmonic maps and vector fields.
result All Ricci solitons on (F4,g) are expanding and non-gradient. 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 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.
Kaimakamis and Panagiotidou in \cite{KP} introduced the notion of ∗-Ricci soliton and studied the real hypersurfaces of a non-flat complex space form admitting a ∗-Ricci soliton whose potential vector field is the structure vector field. In this article, we consider that a real hypersurface of a non-flat complex …
Some observations about the local and global generality of gradient Kahler Ricci solitons are made, including the existence of a canonically associated holomorphic volume form and vector field, the local generality of solutions with a prescribed holomorphic volume form and vector field, and the existence of Poincare co…
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. Study Kähler-Ricci flow on manifolds with singularities.
problem Behavior of Kähler-Ricci flow on manifolds with finite-time singularities.
method Use of holomorphic vector fields to prove estimates.
result Proves estimates related to previous work on the flow.
Study on gradient pseudo-Ricci solitons on real hypersurfaces.
problem Characterize gradient pseudo-Ricci solitons on real hypersurfaces.
method Analyze real hypersurfaces in complex space forms with specific eigen properties of the Ricci tensor.
result Show existence of non-trivial gradient pseudo-Ricci solitons on 3D ruled real hypersurfaces.
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 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…
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.
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.
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.
The concept of the Ricci soliton was introduced by Hamilton. Ricci soliton is defined by vector field and it's a natural generalization of Einstein metric. We have shown earlier that the vector field of Ricci soliton is an infinitesimal harmonic transformation. In our paper, we survey Ricci solitons geometry as an appl…
Considering pseudo-Riemannian g-natural metrics on tangent bundles, we prove that the condition of being Ricci soliton is hereditary in the sense that a Ricci soliton structure on the tangent bundle gives rise to a Ricci soliton structure on the base manifold. Restricting ourselves to some class of pseudo-Riemannian …
Sharp inequalities and solitons studied in statistical submersions.
problem Understanding geometric properties of statistical submersions.
method Proving sharp inequalities and establishing geometrical properties of statistical submersions.
result Characterization of fibers as Ricci-Bourguignon solitons with conformal vector field.
Study properties of 3D almost η-Ricci solitons with diagonal metrics.
problem Characterize 3D almost η-Ricci solitons with diagonal metrics.
method Analyzes manifold properties under specific assumptions and constraints.
result Determines potential vector field and constraints on the metric.
Characterizes Lorentzian manifolds with semi-symmetric metric connections.
problem Characterizing Lorentzian manifolds with specific metric connections.
method Analyzing semi-symmetric metric connections with vanishing curvature and recurrent torsion.
result Establishes conditions for perfect fluid and generalized Robertson-Walker spacetimes.
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 purpose of this article is to study implications of a Ricci soliton warped product manifold to its base and fiber manifolds. First, it is proved that if a warped product manifold is Ricci soliton then its factors are Ricci soliton. Then we study Ricci soliton on warped product manifolds admitting either a conformal…
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 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 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.
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. Local classification of 4D Ricci solitons with specific algebra properties.
problem Classifying 4D Ricci solitons with a 2D Abelian Killing algebra.
method Local classification under specific curvature and symmetry conditions.
result Classification of Ricci solitons with orthogonally intransitive 2D Abelian Killing algebra.
Study projective symmetries in Finsler spaces, showing reductions and constant flag curvature.
problem Exploring projective symmetries in Finsler spaces and their properties.
method Analyzing algebraic sub-algebras and curvature invariants of projective vector fields.
result Closed Finsler spaces with negative Ricci curvature reduce to Killing vector fields.
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.
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 studies Cotton solitons on specific geometric manifolds.
problem Analyzing Cotton solitons in almost Kenmotsu 3-h-manifolds. method Examined potential vector fields and their relationship with the Reeb vector field.
result Steady Cotton solitons on non-Kenmotsu manifolds are locally isometric to H2(−4)imesR. 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 characterizes ∗-Ricci-Bourguignon solitons on Kenmotsu manifolds.
problem Characterizing ∗-Ricci-Bourguignon solitons on Kenmotsu manifolds. method Analyzing conditions for compressing, balancing, or enlarging ∗-Ricci-Bourguignon on Kenmotsu manifolds; estimating curvature properties; featuring with torse-forming vector fields; providing an example. result Found conditions and curvature properties for ∗-Ricci-Bourguignon solitons on Kenmotsu manifolds. Study on Ricci solitons and related metrics in 3D trans-Sasakian manifolds.
problem Exploring metrics like Ricci solitons in 3D trans-Sasakian manifolds.
method Analyzing properties of metrics and structure functions in 3D trans-Sasakian manifolds.
result Characterization of Ricci solitons and scalar curvature in 3D trans-Sasakian manifolds.