Related papers: Killing-Yano tensors and multi-hermitian structure…
We give a detailed account of the geometric correspondence between a smooth complex projective quadric hypersurface $\mathcal{Q}^n$ of dimension $n \geq 3$, and its twistor space $\mathbb{PT}$, defined to be the space of all linear…
Using a Kaluza-Klein-type lift, it is shown how Killing-Yano forms with torsion can remain symmetries of a higher-dimensional geometry, subject to an algebraic condition between the Kaluza-Klein field strength and the Killing-Yano form. The…
We present the conditions when a Killing-Yano tensor becomes a Nambu tensor. We have shown that in the flat space case all Killing-Yano tensors are Nambu tensors. In the case of Taub-NUT metric and Kerr-Newmann metric we found that a…
General higher-dimensional rotating black hole spacetimes of any dimensions admit the Killing and Killing-Yano tensors, which generate the hidden symmetries just as in four-dimensional Kerr spacetime. We study these properties of the black…
We show that the Teukolsky connection, which defines generalized wave operators governing the behavior of massless fields on Einstein spacetimes of Petrov type D, has its origin in a distinguished conformally and GHP covariant connection on…
We show the existence of conformal Killing-Yano tensors on a manifold endowed with a mixed 3-Sasakian structure.
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…
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…
We generalize our recent method for constructing Killing tensors of the second rank to conformal Killing tensors. The method is intended for foliated spacetimes of arbitrary dimension $m$, which have a set of conformal Killing vectors. It…
Let $(G,g)$ be a 4-dimensional Riemannian Lie group with a 2-dimensional left-invariant, conformal foliation $\F$ with minimal leaves. Let $J$ be an almost Hermitian structure on $G$ adapted to the foliation $\F$. We classify such…
A metric projective structure is a manifold equipped with the unparametrised geodesics of some pseudo-Riemannian metric. We make acomprehensive treatment of such structures in the case that there is a projective Weyl curvature nullity…
We study the relation between the existence of null conformal Killing vector fields and existence of compatible complex and para-hypercomplex structures on a pseudo-Riemannian manifold with metric of signature (2,2). We establish first the…
Listing has recently extended results of Kozameh, Newman and Tod for four-dimensional spacetimes and presented a set of necessary and sufficient conditions for a metric to be locally conformally equivalent to an Einstein metric in all…
The remarkable and unexpected separability of the Hamilton-Jacobi and Klein-Gordon equations in the background of a rotating four-dimensional black hole played an important role in the construction of generalisations of the Kerr metric, and…
Geometry of the solution space of the self-dual Yang-Mills (SDYM) equations in Euclidean four-dimensional space is studied. Combining the twistor and group-theoretic approaches, we describe the full infinite-dimensional symmetry group of…
We characterize manifolds which are locally conformally equivalent to either complex projective space or to its negative curvature dual in terms of their Weyl curvature tensor. As a byproduct of this investigation, we classify the…
We investigate higher rank Killing-Yano tensors showing that third rank Killing-Yano tensors are not always trivial objects being possible to construct irreducible Killing tensors from them. We give as an example the Kimura IIC metric were…
Recently, a remarkable new class of spacetimes describing black holes immersed in a non-aligned electromagnetic field has been found. While still of type D, this class goes beyond the famous Pleba\'nski--Demia\'nski family. Here we…
Some years ago Koutras presented a method of constructing a conformal Killing tensor from a pair of orthogonal conformal Killing vectors. When the vector associated with the conformal Killing tensor is a gradient, a Killing tensor (in…
We give a characterization of the $2$-step nilpotent Lie algebras whose corresponding Lie groups admit a left invariant complex structure. This is done by considering separately the cases when the complex structure is 2-step or 3-step…