arXiv research

We introduce in this paper normal twistor equations for differential forms and study their solutions, the so-called normal conformal Killing forms. The twistor equations arise naturally from the canonical normal Cartan connection of conformal geometry. Reductions of its holonomy are related to solutions of the normal t…

Generalizes Lie algebra of conformal Killing vector fields to conformal Killing-Yano forms.

New relation found between ambient obstruction tensor and conformal holonomy.

We study transverse conformal Killing forms on foliations and prove a Gallot-Meyer theorem for foliations. Moreover, we show that on a foliation with $C$-positive normal curvature, if there is a closed basic 1-form $φ$ such that $Δ_Bφ=qCφ$, then the foliation is transversally isometric to the quotient of a $q$-sphere.

Classifies conformal Killing 3-forms on nearly Kähler manifolds.

Researchers solve conformal Killing forms on Kaehler manifolds.

Researchers develop new symmetry operators from conformal Killing-Yano forms.

Given a maximally non-integrable 2-distribution ${\mathcal D}$ on a 5-manifold $M$, it was discovered by P. Nurowski that one can naturally associate a conformal structure $[g]_{\mathcal D}$ of signature (2,3) on $M$. We show that those conformal structures $[g]_{\mathcal D}$ which come about by this construction are c…

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…

Study classifies manifolds with nonpositive curvature and finds conformal Killing forms.

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…

Survey on invariant conformal Killing forms on Lie groups.

Study L2-transverse conformal Killing forms on foliated manifolds.

BGG-equations are geometric overdetermined systems of PDEs on parabolic geometries. Normal solutions of BGG-equations are particularly interesting and we give a simple formula for the necessary and sufficient additional integrability conditions on a solution. We then discuss a procedure for coupling known solutions of …

Study Minkowski formula for conformal Killing-Yano 2-forms in constant curvature spacetimes.

Study conformal Killing forms on specific nilpotent Lie groups.

Study of conformal Killing 2-forms on 4D Lie groups.

BGG-operators form sequences of invariant differential operators and the first of these is overdetermined. Interesting equations in conformal geometry described by these operators are those for Einstein scales, conformal Killing forms and conformal Killing tensors. We present a deformation procedure of the tractor conn…

Study BGG operators on homogeneous conformal geometries.

Harmonic spinors linked to twistor spinors via potential forms and conformal Killing-Yano forms.

On a closed, connected Riemannian manifold with a Kähler foliation of codimension $q=2m$, any transverse Killing $r\ (\geq 2)$-form is parallel (S. D. Jung and M. J. Jung [\ref{JJ2}], Bull. Korean Math. Soc. 49 (2012)). In this paper, we study transverse conformal Killing forms on Kähler foliations and prove that if th…

Study on CKY forms on almost abelian Lie groups, proving parallelism and characterizing non-parallel cases.

A 2-form on a quaternionic-Kahler manifold (M, g) is called compatible (with the quaternionic structure) if it is a section of the direct sum bundle S^2(H) \oplus S^2(E). We construct a connection D on S^2(H) \oplus S^2(E)\oplus TM, which is a prolongation of the conformal-Killing operator acting on compatible 2-forms.…

Extended superalgebras from twistor and Killing spinors in constant curvature and Einstein manifolds.

New approach classifies conformal Killing vector fields for FLRW space-time.

We prove that a compact quaternionic-Kähler manifold of dimension $4n\geq 8$ admitting a conformal-Killing 2-form which is not Killing, is isomorphic to the quaternionic projective space, with its standard quaternionic-Kähler structure.

The study proves that conformal Killing vector fields on manifolds with positive Ricci curvature are non-trivial.

A Killing $p$-form on a Riemannian manifold is a $p$-form whose covariant derivative is totally anti-symmetric. In this paper we give the complete (local) description of 4-dimensional Riemannian manifolds (M,g) carrying non-parallel Killing 2-forms $\varphi$. If $M$ is connected and oriented, we show that there exists …

We use the manifestly conformally invariant description of a Lorentzian conformal structure in terms of a parabolic Cartan geometry in order to introduce a superalgebra structure on the space of twistor spinors and normal conformal vector fields formulated in purely algebraic terms on parallel sections in tractor bundl…

Conditions for conformal Killing vectors in vacuum spacetimes.

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…

New proof shows all conformal fields are Killing on specific spaces.

New characterisation of geodesics in various geometries yields conserved quantities.

Estimates quasi-local mass using Minkowski formula and conformal Killing-Yano forms.

The study finds limits on dimensions of certain scales and fields for conformal manifolds.

We present definitions and properties of conformal Killing, Killing and planarity forms on a Riemannian manifold and determine Tachibana, Killing and planarity numbers as an analog of the well known Betti numbers. We state some set of conditions to characterize these numbers. Moreover, we formulate the main results on …

Researchers derive symmetry operators from twistor spinors in curved spacetime.

The study generalizes twistor spinors to Kähler manifolds and finds bilinear form equations.

In the present paper, we consider the Hodge-de Rham Laplacian that acts on conformal Killing and projective Killing one-forms of a compact Riemannian manifold.

Study Finsler metrics with Killing fields on constant flag curvature surfaces.

We show that the Euclidean Kerr-NUT-(A)dS metric in $2m$ dimensions locally admits $2^m$ hermitian complex structures. These are derived from the existence of a non-degenerate closed conformal Killing-Yano tensor with distinct eigenvalues. More generally, a conformal Killing-Yano tensor, provided its exterior derivativ…

We study the twistor equation on pseudo-Riemannian $Spin^c-$manifolds whose solutions we call charged conformal Killing spinors (CCKS). We derive several integrability conditions for the existence of CCKS and study their relations to spinor bilinears. A construction principle for Lorentzian manifolds admitting CCKS wit…

Characterizes conformal Killing tensors and their Killing scales.

Study on conformal Killing tensors on Riemannian manifolds.

Killing-Yano and conformal Killing-Yano superalgebras are rigid in constant curvature manifolds.

The integrability conditions for the existence of a conformal Killing-Yano tensor of arbitrary order are worked out in all dimensions and expressed in terms of the Weyl tensor. As a consequence, the integrability conditions for the existence of a Killing-Yano tensor are also obtained. By means of such conditions, it is…

New equations connect unit Killing vectors to initial data.

Study second-Chern-Einstein metrics on 4D manifolds, finding Killing vector fields and examples.