Related papers: Killing forms on the five-dimensional Einstein-Sas…
We review the geodesic motion of pseudo-classical spinning particles in curved spaces. Investigating the generalized Killing equations for spinning spaces, we express the constants of motion in terms of Killing-Yano tensors. The general…
The Killing tensors of arbitrary rank on complex projective space with its Fubini-Study metric are determined and it is shown that these spaces are generated by the Killing fields.
Spinor bilinears of generalized spinors and their properties are investigated. Generalized Killing and twistor spinor equations are considered and their relations to the equations satisfied by special types of differential forms are found.…
We present a theorem describing a dual relation between the local geometry of a space admitting a symmetric second-rank Killing tensor, and the local geometry of a space with a metric specified by this Killing tensor. The relation can be…
The role of Killing and Killing-Yano tensors for studying the geodesic motion of the particle and the superparticle in a curved background is reviewed. Additionally the Papadopoulos list [74] for Killing-Yano tensors in G structures is…
New relations involving the Riemann, Ricci and Einstein tensors that have to hold for a given geometry to admit Killing-Yano tensors are described. These relations are then used to introduce novel conserved "currents" involving such…
This paper studies various properties of the Pomeransky-Sen'kov doubly-spinning black ring spacetime. I discuss the structure of the ergoregion, and then go on to demonstrate the separability of the Hamilton-Jacobi equation for null, zero…
In this paper we define the analogue of Calabi--Yau geometry for generic $D=4$, $\mathcal{N}=2$ flux backgrounds in type II supergravity and M-theory. We show that solutions of the Killing spinor equations are in one-to-one correspondence…
The seven and nine dimensional geometries associated with certain classes of supersymmetric $AdS_3$ and $AdS_2$ solutions of type IIB and D=11 supergravity, respectively, have many similarities with Sasaki-Einstein geometry. We further…
Through an exhaustive search, we produce a 5-parameter family of propagation identities for the closed conformal Killing-Yano equation on 2-forms, which hold on an Einstein cosmological vacuum spacetime in any dimension $n>4$. It is…
We discuss conserved currents constructed from the Cotton tensor and (conformal) Killing-Yano tensors (KYTs). We consider the corresponding charges generally and then exemplify with the four-dimensional Pleba\'nski-Demia\'nski metric where…
Killing-Yano tensors are natural generalizations of Killing vectors. We investigate whether Killing-Yano tensors form a graded Lie algebra with respect to the Schouten-Nijenhuis bracket. We find that this proposition does not hold in…
Using Killing-Yano symmetries, we construct conserved charges of spacetimes that asymptotically approach to the flat or Anti-de Sitter spaces only in certain directions. In D dimensions, this allows one to define gravitational charges (such…
We examine hidden symmetry and its relation to the separability of the Maxwell equation on the Wahlquist spacetime. After seeing that the Wahlquist spacetime is a type-D spacetime whose repeated principal null directions are shear-free and…
We discuss novel generalisations of Killing tensors, which are introduced by considering rational first integrals of geodesic equations. We introduce the notion of inconstructible generalised Killing tensors, which cannot be constructed…
We study 7D maximally supersymmetric Yang-Mills theory on curved manifolds that admit Killing spinors. If the manifold admits at least two Killing spinors (Sasaki-Einstein manifolds) we are able to rewrite the supersymmetric theory in terms…
We present the twisted covariant form hierarchies (TCFH) of type IIA and IIB 10-dimensional supergravities and show that all form bilinears of supersymmetric backgrounds satisfy the conformal Killing-Yano equation with respect to a TCFH…
Conformal rescaling of conformal Yano--Killing tensors and relations between Yano and CYK tensors are discussed. Pullback of these objects to a submanifold is used to construct all solutions of a CYK equation in anti-de Sitter and de Sitter…
The Kerr-Taub-NUT spacetime in the Kaluza-Klein theory represents a localized stationary and axisymmetric object in four dimensions from the Kaluza-Klein viewpoint. That is, it harbors companion electromagnetic and dilaton fields, thereby…
This paper is the initial part of a comprehensive study of spacetimes that admit the canonical forms of Killing tensor in General Relativity. The general scope of the study is to derive either new exact solutions of Einstein's equations…