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 study proves that conformal Killing vector fields on manifolds with positive Ricci curvature are non-trivial.
problem Investigating conformal Killing vector fields on manifolds under curvature pinching conditions.
method Establishing a new Bochner-type identity and using Moser iteration for gradient estimates.
result Conformal Killing vector fields are non-trivial on manifolds with positive Ricci curvature.
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.
Solves numerical computation of Killing and conformal Killing vector fields on compact Riemannian manifolds.
problem Overdetermined systems of PDE make numerical computation difficult.
method Reduces to symmetric eigenvalue problem solved by finite element techniques.
result Valid in any dimension and for arbitrary compact Riemannian manifolds.
We provide a generalization of the Lie algebra of conformal Killing vector fields to conformal Killing-Yano forms. A new Lie bracket for conformal Killing-Yano forms that corresponds to slightly modified Schouten-Nijenhuis bracket of differential forms is proposed. We show that conformal Killing-Yano forms satisfy a gr…
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.
Killing-Yano and conformal Killing-Yano superalgebras are rigid in constant curvature manifolds.
problem Understanding the rigidity of Killing-Yano and conformal Killing-Yano superalgebras in constant curvature manifolds.
method Defining Z-gradations and filtrations, showing trivial second cohomology groups, and proving non-deformability. result Killing-Yano and conformal Killing-Yano superalgebras are rigid and correspond to geometric invariants of constant curvature manifolds.
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.
Study on conformal vector fields on Lie groups, proving properties and providing examples.
problem Characterizing conformal vector fields on Lie groups with pseudo-Riemannian metrics.
method Investigation of left-invariant conformal vector fields on Lie groups with specific metrics, proving properties and providing examples.
result Necessary conditions and examples of non-Killing conformal vector fields on non-unimodular Lie groups.
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.
Killing tensors on tori are shown to be polynomial in the metric and Killing vector fields.
problem Characterizing Killing tensors on conformally flat tori.
method Analyzing Killing tensors on tori with a conformal factor depending on one variable.
result Killing tensors on such tori are polynomial in the metric and Killing vector fields.
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.
Using twistor methods, we explicitly construct all local forms of four--dimensional real analytic neutral signature anti--self--dual conformal structures (M,[g]) with a null conformal Killing vector. We show that M is foliated by anti-self-dual null surfaces, and the two-dimensional leaf space inherits a natural pr…
Conditions for conformal Killing vectors in vacuum spacetimes.
problem Finding conditions for conformal Killing vectors in vacuum spacetimes.
method Classical argument to identify a suitable propagation identity and check well-posedness of the initial value problem.
result Necessary and sufficient conditions for conformal Killing initial data (CKID) are found, extending known Killing initial data (KID).
New proof shows all conformal vector fields on complex hyperbolic space are Killing.
problem Proving all conformal vector fields on complex hyperbolic space are Killing.
method Local, analytic, and constructive approach using Lie group model and partial differential equations.
result Every conformal vector field on complex hyperbolic space is Killing.
Conformal Killing forms are a natural generalization of conformal vector fields on Riemannian manifolds. They are defined as sections in the kernel of a conformally invariant first order differential operator. We show the existence of conformal Killing forms on nearly Kaehler and weak G_2-manifolds. Moreover, we give a…
A space has the maximal number of CKVs if and only if it is conformally flat.
problem Determining the necessity of conformal flatness for maximal CKVs.
method Analyzing properties of conformally flat spaces and CKVs.
result Conformal flatness is a necessary and sufficient condition for maximal CKVs.
Study explores geometric implications of timelike conformal Killing vectors.
problem Exploring geometric implications of timelike conformal Killing vectors.
method Investigates geometric consequences of timelike conformal Killing vector fields on globally hyperbolic spacetimes.
result Provides complementary result to Galloway and Vega's main theorem.
The study extends and generalizes a result about quasi Einstein manifolds, proving conditions for Killing vector fields.
problem Characterizing conditions for Killing vector fields in quasi Einstein manifolds.
method Extending and generalizing Cochran's result, proving conditions for Killing vector fields under specific integrals and conformal conditions.
result Conditions for Killing vector fields in quasi Einstein manifolds, including integral identities and global isometry to spheres.
We construct a conformally invariant vector bundle connection such that its equation of parallel transport is a first order system that gives a prolongation of the conformal Killing equation on differential forms. Parallel sections of this connection are related bijectively to solutions of the conformal Killing equatio…
Paper extends isoperimetric inequalities for non-starshaped hypersurfaces.
problem Isoperimetric inequalities for non-starshaped hypersurfaces.
method Volume preserving and area decreasing mean curvature flow with conformal Killing vector fields.
result Established isoperimetric inequalities for a broader class of hypersurfaces.
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.
We show that the first-order symmetry operators of twistor spinors can be constructed from conformal Killing-Yano forms in conformally-flat backgrounds. We express the conditions on conformal Killing-Yano forms to obtain mutually commuting symmetry operators of twistor spinors. Conformal superalgebras which consist of …
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.
Characterizes conformal Killing tensors and their Killing scales.
problem Characterizing conformal Killing tensors and their Killing scales.
method Differential prolongation using conformally invariant tractor calculus.
result Provides an invariant characterisation of Einstein Killing scales.
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. Researchers identify surfaces with special fluid flow fields.
problem Understanding fluid flows on curved surfaces.
method Defined and analyzed hydrodynamic Killing vector fields (HKVF) on surfaces.
result Any connected, orientable surface with HKVF is conformally equivalent to one of 14 canonical Riemann surfaces.
Study of Lorentzian surfaces with Killing fields, characterizing their conformal classes.
problem Characterizing conformal classes of Lorentzian surfaces with Killing fields.
method Defining a map associating conformal classes to vector fields on the circle, analyzing finite-dimensional fibers.
result Finite-dimensional fibers of the map, allowing characterization of conformal classes.
A vector field on a Riemannian manifold is called conformal Killing if it generates one-parameter group of conformal transformations. The class of conformal Killing symmetric tensor fields of an arbitrary rank is a natural generalization of the class of conformal Killing vector fields, and appears in different geometri…
Generalizing Riemannian theorems of Anderson-Herzlich and Biquard, we show that two (n+1)-dimensional stationary vacuum space-times (possibly with cosmological constant Λ∈R) that coincide up to order one along a timelike hypersurface $\mycal T$ are isometric in a neighbourhood of $\mycal T$. We further prove th…
We prove the existence and uniqueness of graphs with prescribed mean curvature function in a large class of Riemannian manifolds which comprises spaces endowed with a conformal Killing vector field.
New method solves Einstein constraint equations with non-constant mean curvature.
problem Solving Einstein constraint equations with non-constant mean curvature.
method Drift method, which compensates for greater analytic complexity.
result Method can handle metrics with conformal Killing but not true Killing vector fields.
Vacuum spacetimes with conformal symmetry are rigid and split.
problem Understanding the rigidity of vacuum spacetimes under conformal symmetry.
method Analyzing globally hyperbolic vacuum spacetimes with timelike conformal Killing fields.
result Rigidity result for vacuum spacetimes with compact Cauchy surfaces and timelike conformal Killing fields.
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.
We study first and second order conformal symmetries of the Yamabe Laplacian on a general pseudo-Riemannian manifold and of the Paneitz operator on Einstein spaces. We show that first order conformal symmetries of the Yamabe operator induce second order conformal symmetries. We show that on an Einstein space every conf…
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.
New proof shows all conformal fields are Killing on specific spaces.
problem Infinitesimal conformal rigidity on Damek-Ricci spaces.
method Formulated as PDEs, analyzed locally and directly.
result Constructive proof of rigidity without global methods.
Study second-Chern-Einstein metrics on 4D manifolds, finding Killing vector fields and examples.
problem Investigate second-Chern-Einstein metrics on 4D almost-Hermitian manifolds.
method Analyze compact and unimodular almost-abelian Lie algebras, use Killing vector fields and parallel non-zero Lee forms.
result Describe 4D compact second-Chern-Einstein locally conformally symplectic manifolds and classify unimodular almost-abelian Lie algebras with second-Chern-Einstein metrics.
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.
In this paper we introduce and study a geometric heat flow to find Killing vector fields on closed Riemannian manifolds with positive sectional curvature. We study its various properties, prove the global existence of the solution of this flow, discuss its convergence and possible applications, and its relation to the …
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.
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.
Characterizes spacetimes using doubly torqued vectors.
problem Classifying spacetimes based on their geometric properties.
method Characterization through doubly torqued vectors and their properties.
result Doubly twisted and Kundt spacetimes can be characterized.
The paper studies conformally Einstein-Maxwell Kähler metrics and automorphism group structure.
problem Analyzing conformally Einstein-Maxwell Kähler metrics and their automorphism groups.
method Using a Hessian formula for the Calabi functional and extending the Lichnerowicz-Matsushima Theorem.
result Proves a reductiveness result of the reduced Lie algebra of holomorphic vector fields for conformally Einstein-Maxwell Kähler manifolds.
We consider several transformation groups of a locally conformally Kähler manifold and discuss their inter-relations. Among other results, we prove that all conformal vector fields on a compact Vaisman manifold which is neither locally conformally hyperkähler nor a diagonal Hopf manifold are Killing, holomorphic and th…
A characterization of the Kerr-NUT-(A)de Sitter metric among four dimensional Λ-vacuum spacetimes admitting a Killing vector is obtained in terms of the proportionality of the self-dual Weyl tensor and a natural self-dual double two-form constructed from the Killing vector. This result recovers and extends a previous c…
For a conformal vector field ξ on a Riemannian manifold, we say that a point is essential if there is no local metric in the conformal class for which ξ is Killing. We show that the only essential points are isolated zeros of ξ. As an application, we show that every connected component of the zero set of ξ is t…
Study on vector fields on Lie groups reveals surprising algebraic coincidences.
problem Characterizing vector fields on Lie groups with Riemannian metrics.
method Algebraic and geometric analysis of left-invariant vector fields on nilpotent Lie groups.
result Spaces of Killing, one-harmonic, and conformal vector fields coincide with the center of the Lie algebra on nilpotent Lie groups.