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.
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.
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 Schwarzians in the Heisenberg group, introducing new definitions and characterizing contact conformal vector fields.
problem Exploring Schwarzians in the Heisenberg group and their properties.
method Introducing two definitions of Schwarzians (CR and classical) and studying their kernels and cocycle conditions.
result Characterization of contact conformal vector fields and results in subelliptic PDEs.
Geodesic vector fields on flat 3-manifolds are related to contact structures.
problem Understanding geodesic vector fields on flat 3-manifolds.
method Analyzing geodesic and Reeb vector fields on flat 3-manifolds.
result Geodesic vector fields on closed flat 3-manifolds are Reeb vector fields of contact forms.
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. Study on solitons in complex Riemannian manifolds with specific properties.
problem Investigating solitons on specific types of complex Riemannian manifolds.
method Introduced and analyzed almost Riemann solitons on almost contact complex Riemannian manifolds with a vertical potential.
result Derived curvature properties and constructed an explicit example of dimension five.
The paper examines timelike conformal fields on 3-manifolds and finds they are rigidly tied to specific geometric structures.
problem Investigating timelike conformal vector fields on closed Lorentzian 3-manifolds.
method Performing conformal changes to unit vectors and analyzing the resulting flows through stable Hamiltonian structures and cohomology.
result Timelike conformal vector fields on 3-manifolds are either Reeb vector fields of Sasakian or co-Kähler structures.
Akyol M.A. [Conformal anti-invariant submersions from cosymplectic manifolds, Hacettepe Journal of Mathematics and Statistic, 46(2), (2017), 177-192.] defined and studied conformal anti-invariant submersions from cosymplectic manifolds. The aim of the present paper is to define and study the notion of conformal slant s…
The paper explores properties of conformal vector fields on almost Kenmotsu manifolds.
problem Characterizing properties of conformal vector fields on almost Kenmotsu manifolds.
method Analyzing conformal vector fields as Reeb vector fields and pointwise collinear, proving manifold properties and existence of warped products.
result Conformal vector fields on almost Kenmotsu manifolds lead to specific manifold structures and properties.
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. The paper studies a new submersion type with specific conditions.
problem Characterizing a new submersion type in Riemannian geometry.
method Examining semi-invariant conformal ζ⊥-Riemannian submersions with horizontal Reeb vector field. result Conditions for the submersions to be totally geodesic and harmonic.
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.
First, we prove that indefinite Sasakian manifolds do not admit any screen conformal r-null submanifolds, tangent to the structure vector field. We, therefore, define a special class of null submanifolds, called; {\it contact screen conformal} r-null submanifold of indefinite Sasakian manifolds. Several characteriz…
The study characterizes and classifies specific types of manifolds using conformal and quasi-Einstein properties.
problem Characterizing and classifying manifolds with specific geometric properties.
method Analyzing warped products, contact manifolds, and semi-Riemannian manifolds.
result Characterizations and classifications of weakly conformally flat and quasi-Einstein manifolds.
We introduce two classes of null hypersurfaces of an indefinite Sasakian manifold, (M,φ,ζ,η), tangent to the characteristic vector field ζ, called; {\it contact screen conformal} and {\it contact screen umbilic} null hypersurfaces. These hypersurfaces come in to fill the existing gap in screen…
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.
We consider the Lie algebra of all vector fields on a contact manifold as a module over the Lie subalgebra of contact vector fields. This module is split into a direct sum of two submodules: the contact algebra itself and the space of tangent vector fields. We study the geometric nature of these two modules.
In this article we develop some elementary aspects of a theory of symmetry in sub-Lorentzian geometry. First of all we construct invariants characterizing isometric classes of sub-Lorentzian contact 3 manifolds. Next we characterize vector fields which generate isometric and conformal symmetries in general sub-Lorentzi…
We introduce higher order mean curvatures of screen almost conformal (SAC) half-lightlike submanifolds of indefinite contact manifolds, admitting a semi-symmetric non-metric connection, and use them to generalize some known results of [6]. Also, we derive a new set of integration formulae via the divergence of some spe…
Contact Lie systems analyze integral curves of Hamiltonian vector fields.
problem Analyzing integral curves of Hamiltonian vector fields.
method Define and study contact Lie systems, including conservative systems.
result Develop Liouville theorems, contact reductions, and Gromov non-squeezing theorems.
The paper simplifies proofs and characterizes contact structures in 3D.
problem Contact structures induced by geodesic vector fields in 3D.
method New proofs and characterizations of contact structures.
result Contact structures in 3D are universally tight under certain conditions.
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. Conformal vector fields on LCP manifolds are orthogonal and Killing.
problem Understanding conformal vector fields on specific geometric manifolds.
method Analyzing properties of conformal vector fields on compact locally conformally product manifolds.
result Conformal vector fields are orthogonal to the flat distribution and Killing.
The paper proves that certain modified conformal vector fields are trivial on compact and non-compact manifolds.
problem Proving triviality of modified conformal vector fields on Riemannian manifolds.
method Analyzing properties of homothetic, conformal, and gradient vector fields on compact and non-compact manifolds.
result Established conditions under which m-modified conformal vector fields are trivial. New approach classifies conformal Killing vector fields for FLRW space-time.
problem Classifying conformal Killing vector fields for FLRW space-time.
method Introduced new perspective on conformal Killing vector fields for FLRW space-time, considering three cases for the conformal factor.
result Nine conformal vector fields on FLRW, six of which are Killing and the rest non-Killing.
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 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.
Geometric structures on NQ-manifolds, i.e.~non-negatively graded manifolds with an homological vector field, encode non-graded geometric data on Lie algebroids and their higher analogues. A particularly relevant class of structures consists of vector bundle valued differential forms. Symplectic forms, contac…
Unified Jacobi coupling construction for various geometric settings.
problem Constructing Jacobi structures on associated bundles.
method Extending Sternberg--Weinstein coupling to Jacobi geometry.
result Associated bundles inherit Jacobi structures from base spaces.
Conformal vector fields on lcK manifolds are shown to be Killing or holomorphic.
problem Characterizing conformal vector fields on lcK manifolds.
method Analyzing properties of conformal vector fields on compact lcK manifolds.
result Conformal vector fields on compact lcK manifolds are either Killing or holomorphic.
We provide some examples of harmonic unit vector fields as normalized gradients of isoparametric functions from a K-contact geometry setting.
Survey reviews Hamilton-Jacobi theory in various geometric settings, focusing on Jacobi and Leibniz identities.
problem Analyzing Hamilton-Jacobi theory across different geometric backgrounds.
method Geometric review of Hamilton-Jacobi theory, focusing on Jacobi and Leibniz identities.
result Novel Hamilton-Jacobi equation for conformal Hamiltonian vector fields.
We provide obstructions to the existence of conformally Anosov Reeb flows on a 3-manifold that partially generalize similar obstructions to Anosov Reeb flows. In particular, we show S3 does not admit conformally Anosov Reeb flows. We also give a Riemannian geometric condition on a metric compatible with a c…
We consider a closed orientable Riemannian 3-manifold (M,g) and a vector field X with unit norm whose integral curves are geodesics of g. Any such vector field determines naturally a 2-plane bundle contained in the kernel of the contact form of the geodesic flow of g. We study when this 2-plane bundle remains i…
The study classifies spaces with specific conformal vector fields.
problem Characterizing closed vacuum static spaces with non-Killing conformal vector fields.
method Provided characterizations and established an identity involving the characteristic function.
result Derived a rigidity theorem and classified spaces with the vector field.
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…
Develops Hamilton-Jacobi theory for non-conservative field theories in k-contact geometry.
problem Analyzes non-conservative field theories, especially dissipative systems.
method Introduces evolution k-contact k-vector fields and develops two Hamilton-Jacobi theories.
result Recover ordinary contact Hamilton-Jacobi theory as k=1, and enlarges application range.
Study proves conformal vector fields on certain Finsler manifolds are Killing fields.
problem Characterizing conformal vector fields on compact homogeneous Finsler manifolds.
method Analyzes properties of conformal vector fields and homogeneous Finsler metrics.
result Conformal vector fields on compact homogeneous Finsler manifolds are Killing fields.
The abstract proves that certain Reeb vector fields on 3-manifolds have Birkhoff sections.
problem Existence of Birkhoff sections for Reeb vector fields on 3-manifolds.
method Showed existence of Birkhoff sections for Reeb vector fields satisfying Kupka-Smale condition.
result Reeb vector fields on closed 3-manifolds with Kupka-Smale condition admit Birkhoff sections.
We show that φ-invariant submanifolds of metric contact pairs with orthogonal characteristic foliations make constant angles with the Reeb vector fields. Our main result is that for the normal case such submanifolds of dimension at least 2 are all minimal. We prove that an odd-dimensional φ-invariant submanifold …
In this paper, we investigated the behavior of left-invariant conformal vector fields on Lie groups with left-invariant pseudo-Riemannian metrics. First of all, we prove that conformal vector fields on pseudo-Riemannian unimodular Lie groups are Killing. Then we obtain a necessary condition for a pseudo-Rimennian non-u…
Let M be an odd-dimensional Euclidean space endowed with a contact 1-form α. We investigate the space of symmetric contravariant tensor fields on M as a module over the Lie algebra of contact vector fields, i.e. over the Lie subalgebra made up by those vector fields that preserve the contact structure. If we cons…
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. Study null conformal Killing vector fields on complex surfaces.
problem Characterize pseudo-Hermitian surfaces with null vector fields.
method Analyze topological types and use vector fields to define para-hyperhermitian structures.
result Classify compact four-manifolds with orthogonal null Killing vector fields.
The paper classifies K-contact forms on 3-manifolds and connects their orbits to spectral invariants.
problem Classifying K-contact forms with specific properties on 3-manifolds.
method Analyzing the Reeb vector field and its orbits, proving diffeomorphism results, and relating to spectral invariants.
result Compact 3-manifolds carrying such K-contact forms are diffeomorphic to lens spaces with specific orbit properties.
We consider a contact manifold with a pseudo-Riemannian metric and define a contact vector field intrinsically associated to this pair of structures. We call this new differential invariant the contact Riemannian curl. On a Riemannian manifold, Killing vector fields are those that annihilate the metric; a Killing 1-f…
The study explores (m,ρ)-quasi-Einstein structures on contact metric manifolds.
problem Exploring (m,ρ)-quasi-Einstein structures in contact geometry. method Proving properties of (m,ρ)-quasi-Einstein structures on contact metric manifolds. result Compact contact or H-contact metric manifolds with (m,ρ)-quasi-Einstein structures have specific properties.