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We consider spin manifolds with an Einstein metric, either Riemannian or indefinite, for which there exists a Killing spinor. We describe the intrinsic geometry of nondegenerate hypersurfaces in terms of a PDE satisfied by a pair of induced…
It is well known that 4-dimensional Kerr-NUT-AdS spacetime possesses the hidden symmetry associated with the Killing-Yano tensor. This tensor is "universal" in the sense that there exist coordinates where it does not depend on any of the…
In this contribution we have collected some facts about Killing and Killing-Yano tensors that we feel are of general interest for researchers working on problems that rely on differential geometry. We also include some of our recent studies…
We give a new characterisation of the unparametrised geodesics, or distinguished curves, for affine, pseudo-Riemannian, conformal, and projective geometry. This is a type of moving incidence relation. The characterisation is used to provide…
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…
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…
We discuss a recently proposed geometric method for constructing a nontrivial Killing tensor of rank two in a foliated spacetime of codimension one that lifts trivial Killing tensors from slices to the entire manifold. The existence of…
We investigate the hidden symmetries of the Kerr-Newman, of the D=5 minimal gauged supergravity which admits a Killing-Maxwell system in the sense of Carter and of higher dimensional spacetimes in the presence of Killing-Yano torsion. We…
The Minkowski tensors are the natural tensor-valued generalizations of the intrinsic volumes of convex bodies. We prove two complete sets of integral geometric formulae, so called kinematic and Crofton formulae, for these Minkowski tensors.…
We illustrate a rigorous approach to express the totally symmetric isotropic tensors of arbitrary rank in the $n$-dimensional Euclidean space as a linear combination of products of Kronecker deltas. By making full use of the symmetries, one…
We employ the G-structure formalism to study supersymmetric solutions of minimal and SU(2) gauged supergravities in seven dimensions admitting Killing spinors with associated timelike Killing vector. The most general such Killing spinor…
In this paper we solve the problem of finding integrals of equations determining the Killing tensors on an $n$ -dimensional differentiable manifold $M$ endowed with an equiaffine $ SL(n, R) $ -structure and discuss possible applications of…
The fundamental tool in the classification of orthogonal coordinate systems in which the Hamilton-Jacobi and other prominent equations can be solved by a separation of variables are second order Killing tensors which satisfy the Nijenhuis…
We present a systematic prolongation procedure and its implementation for Killing two-tensors, especially in the locally symmetric case. We use the resulting machinery to elucidate the natural quadratic mapping from Killing fields to…
We propose a generalization of the (conformal) Killing-Yano equations relevant to D=5 minimal gauged supergravity. The generalization stems from the fact that the dual of the Maxwell flux, the 3-form *F, couples naturally to particles in…
We explore the Euclidean supersymmetric solutions admitting the self-dual gauge field in the framework of ${\cal N}=2$ minimal gauged supergravity in four dimensions. According to the classification scheme utilizing the spinorial geometry…
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…
New kinds of supersymmetry arise in supersymmetric $\sg$-models describing the motion of spinning point-particles in classical backgrounds, for example black-holes, or the dynamics of monopoles. Their geometric origin is the existence of…
A set of simple rules for constructing the maximal (e.g. analytic) extensions for any metric with a Killing field in an (effectively) two-dimensional spacetime is formulated. The application of these rules is extremely straightforward, as…
The existence of Killing-Yano tensors on space-times can be probed by spinning particles. Specifically, Dirac particles possess new fermionic constants of motion corresponding to non-standard supersymmetries on the particle worldline. A…