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.
Affine vector fields on pseudo-Kähler manifolds are symplectic.
problem Characterize affine vector fields on compact pseudo-Kähler manifolds.
method Two proofs provided, showing affine vector fields are symplectic and discuss properties of Lie derivatives.
result Affine vector fields on compact pseudo-Kähler manifolds are symplectic.
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 …
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.
Killing fields on compact pseudo-Kähler manifolds are holomorphic.
problem Characterizing Killing fields on compact pseudo-Kähler manifolds.
method Detailed explanation and argumentation of why a previous claim was incomplete.
result Killing fields on compact pseudo-Kähler manifolds are holomorphic.
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…
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.
In this paper, we define a semi-symmetric metric Killing vector field, then study semi-symmetric metric Killing vector fields on warped and multiply warped products with a semi-symmetric metric connection. We also study Killing and 2-Killing vector fields on multiply warped products.
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 consider Killing vector fields on standard static space-times and obtain equations for a vector field on a standard static space-time to be Killing. We also provide a characterization of Killing vector fields on standard static space-times with compact Riemannian parts.
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.
Researchers found indecomposable Killing tensor fields on quaternionic projective spaces.
problem Characterizing Killing tensor fields on projective spaces.
method Analyzing Killing tensor fields on quaternionic and complex projective spaces, proving algebraic properties.
result Generated algebras of Killing tensor fields on quaternionic and complex projective spaces.
The paper studies deformations of Kundt metrics using nil-Killing vector fields.
problem Deformations of Kundt metrics in the direction of type III tensors.
method Characterizations within the Kundt class using nil-Killing vector fields.
result Theorem classifying algebraic stability of tensors and sufficient criteria for preserving spi's.
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.
Zermelo deformation preserves geodesics and curvature in Finsler metrics.
problem Behavior of geodesics and curvature in Finsler metrics under Zermelo deformation.
method Zermelo deformation with Killing vector fields.
result Zermelo deformation preserves local symmetry in locally symmetric Finsler metrics.
The study explores mixed Killing vector fields on almost coKähler manifolds.
problem Characterizing mixed Killing vector fields on almost coKähler manifolds.
method Generalized Bochner's theorem for mixed Killing vector fields and studied in the context of almost coKähler structures.
result The Reeb vector field on an almost coKähler manifold is mixed Killing if and only if the operator h=0. 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.
Given a compatible vector field on a compact connected almost-complex manifold, we show in this article that the multiplicities of eigenvalues among the zero point set of this vector field have intimate relations. We highlight a special case of our result and reinterpret it as a vanishing-type result in the framework o…
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.
The present article provides a study of 2−Killing vector fields on warped product manifolds as well as characterization of this structure on standard static and generalized Robertson-Walker space-times. Some conditions for a 2−Killing vector field on a warped product manifold to be parallel are obtained. Moreover, …
Study Riemannian Q-manifolds with Killing vector fields, finding them unimodular.
problem Defining and studying Riemannian structures on Q-manifolds.
method Define Riemannian Q-manifolds and show their unimodularity.
result Riemannian Q-manifolds are unimodular.
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 characterizes 2-Killing vector fields on complex spacetimes.
problem Characterize 2-Killing vector fields on multiply twisted product spacetimes. method Determine nonlinear differential equations, find twisted functions, provide solutions, and construct examples.
result Completely describe 2-Killing vector fields and twisted functions on multiply twisted product spacetimes. Study on Killing vector fields with constant length on Riemannian manifolds.
problem Properties of Killing vector fields of constant length on Riemannian manifolds.
method Analysis of the linear operator ad(X) and its spectrum.
result The linear operator ad(X) has a pure imaginary spectrum.
Study on Finsler spacetimes with timelike Killing vectors, introducing stationary splitting.
problem Characterizing Finsler spacetimes with timelike Killing vectors.
method Introducing a new class of stationary splitting Finsler spacetimes and characterizing their properties.
result A Finsler spacetime with a timelike Killing vector field is locally a stationary splitting.
Holomorphic tensors on Vaisman manifolds are invariant under the Lee field.
problem Characterizing holomorphic tensors on Vaisman manifolds.
method Using the parallelism of the Lee form and properties of the Lee field.
result The Kodaira dimension of Vaisman manifolds is invariant under certain quotients.
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 term "special biconformal change" refers, basically, to the situation where a given nontrivial real-holomorphic vector field on a complex manifold is a gradient relative to two Kähler metrics, and, simultaneously, an eigenvector of one of the metrics treated, with the aid of the other, as an endomorphism of the tan…
Killing vector fields of a closed homogeneous and isotropic universe are studied. It is shown that in general case there is no time-like Killing vector fields in such a universe. Two exceptional cases are revealed.
The tangent bundle of a Riemannian manifold (M,g) with non-degenerated g-natural metric G that admits a Killing vector field is investigated. Using Taylor's formula (TM,G) is decomposed into four classes that are investigated separately. The equivalence of the existence of Killing vector field on M and TM is proved. Ke…
Researchers found non-Killing tensor fields on certain symmetric spaces.
problem Understanding Killing tensors on all Riemannian symmetric spaces.
method Constructed explicit examples of quadratic Killing tensors on quaternionic and Cayley projective spaces.
result Quadratic Killing tensors can be non-Killing on some symmetric spaces.
A supermanifold M is canonically associated to any pseudo Riemannian spin manifold (M_0,g_0). Extending the metric g_0 to a field g of bilinear forms g(p) on T_p M, p\in M_0, the pseudo Riemannian supergeometry of (M,g) is formulated as G-structure on M, where G is a supergroup with even part G_0\cong Spin(k,l); (k,l) …
The moduli space of Hermitian-Einstein connections on certain manifolds has a strong Kähler with torsion structure.
problem Characterizing the moduli space of Hermitian-Einstein connections on manifolds with a dilaton field.
method Demonstrates the existence of a strong Kähler with torsion structure on the moduli space under specific conditions on the Lee form and dilaton field.
result The moduli space admits an induced holomorphic and Killing vector field when the manifold has a holomorphic and Killing vector field invariant under the dilaton.
Study examines causal properties of Finsler spacetimes with cone Killing vectors.
problem Characterize causality in Finsler spacetimes with specific Killing vectors.
method Explores the relationship between wind Riemannian structures and spacetimes with cone Killing vectors, focusing on Finsler-Kropina metrics.
result Characterizes causality properties using metric-type properties of Finslerian structures.
This research bridges Killing vectors and Lie algebras through induced vector fields.
problem Understanding the relationship between Killing vector fields and Lie algebras.
method Defining and exploring induced vector fields to connect Killing vector fields with isometry Lie groups.
result Established a new connection between Killing vector fields and Lie algebras.
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…
In this paper, we prove that, if a full irreducible infinite dimensional anti-Kaehler isoparametric submanifold of codimension greater than one has J-diagonalizable shape operators, then it is an orbit of the action of a Banach Lie group generated by one-parameter transformation groups induced by holomorphic Killing …
The study extends Hano's theorem to semi-Riemannian product manifolds with specific conditions.
problem Extending Hano's theorem to manifolds with indefinite metrics.
method Generalization of Hano's theorem to semi-Riemannian product manifolds with specific conditions.
result The assumption on the factors is necessary for the generalization.
Study torsion's impact on 2D affine Killing vectors on homogeneous surfaces.
problem Effects of torsion on affine Killing vectors on homogeneous surfaces.
method Complete description of Lie algebras of affine Killing vector fields on homogeneous surfaces.
result Complete description of Lie algebras of affine Killing vector fields on homogeneous surfaces.
New method to determine parabolic surfaces invariant under Killing fields.
problem Characterizing parabolic invariant surfaces.
method Clear and practical characterization method for invariant surfaces.
result A new way to determine parabolicity of invariant surfaces.
New curvature obstruction for Killing vector fields on Lorentzian manifolds.
problem Existence of timelike or causal Killing vector fields on Lorentzian manifolds.
method New curvature obstruction in terms of timelike or null sectional curvature.
result Extension of Gauss-Bonnet-Chern obstruction to non-zero timelike sectional curvature.
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.
Extends Killing vector fields to beyond compact Cauchy horizons.
problem Proves existence of Killing vector fields beyond compact Cauchy horizons.
method New unique continuation theorem for wave equations through smooth compact lightlike hypersurfaces; novel Carleman type estimate.
result Killing vector field exists on both sides of the horizon.
We prove that holomorphic normal projective connections on compact complex surfaces are flat. We show that a holomorphic torsion-free affine connection ∇ on a compact complex surface is locally modelled on a translations-invariant affine connection on $\C^2$, except if ∇ is a generic connection on a princ…
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.
The harmonic action functional allows a natural generalisation to semi-Riemannian supergeometry, referred to as superharmonic action, which resembles the supersymmetric sigma models studied in high energy physics. We show that Killing vector fields are infinitesimal supersymmetries of the superharmonic action and prove…
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.