Related papers: Prolongation and Killing two-tensors
The supersymmetric extension of charged point particle's motion is applied to investigate symmetries of gravitational fields and electromagnetic fields. We mainly focus on the role of the Killing- Yano tensors of both usual and generalized…
We construct the Killing(-Yano) tensors for a large class of charged black holes in higher dimensions and study general properties of such tensors, in particular, their behavior under string dualities. Killing(-Yano) tensors encode the…
Generalizing the Lie derivative of smooth tensor fields to distribution-valued tensors, we examine the Killing symmetries and the collineations of the curvature tensors of some distributional domain wall geometries. The chosen geometries…
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…
The paper develops elementary linear algebra methods to compute the determinants of the tensor symmetrizations of quadratic and hermitian forms over fields of good characteristic. Explicit results are given for the partitions $(n)$,…
We study the symmetric tensor rank of multiplication over finite field extensions using linearized polynomials. Via field trace, symmetric linearized polynomials are identified with symmetric bilinear forms and symmetric matrices, allowing…
The class of the two-loop massless crossed boxes, with light-like external legs, is the final unresolved issue in the program of computing the scattering amplitudes of 2 --> 2 massless particles at next-to-next-to-leading order. In this…
The purpose of this present paper is to investigate the geometric structure of regular overdetermined systems of second order with two independent and one dependent variables from the point of view of rank 2 prolongations. Utilizing this…
In these lectures the relations between symmetries, Lie algebras, Killing vectors and Noether's theorem are reviewed. A generalisation of the basic ideas to include velocity-dependend co-ordinate transformations naturally leads to the…
We elaborate on basic properties of generalized Killing-Yano tensors which naturally extend Killing-Yano symmetry in the presence of skew-symmetric torsion. In particular, we discuss their relationship to Killing tensors and the…
We study invariant systems of PDEs defining Killing vector-valued forms, and then we specialize to Killing spinor-valued forms. We give a detailed treatment of their prolongation and integrability conditions by relating the point-wise…
(n+2)-dimensional Lorentzian spacetime which admits irreducible Killing tensors of rank up to n is constructed by applying the Eisenhart lift to the Calogero model.
We put into light the Killing vector fields on $\mathbb R^2$ endowed with a family of diagonal Riemannian metrics. According to certain restrictions on the Lam\'{e} coefficients, we concretely describe the symmetries of the metric.
We consider sequential iterative processes for the common fixed point problem of families of cutter operators on a Hilbert space. These are operators that have the property that, for any point x\inH, the hyperplane through Tx whose normal…
The Rainich problem for the Killing-Yano tensors posed by Collinson \cite{col} is solved. In intermediate steps, we first obtain the necessary and sufficient conditions for a 2+2 almost-product structure to determine the principal 2--planes…
In this paper we discuss the consequences of a Killing symmetry on the local geometrical structure of four-dimensional spacetimes. We have adopted the point of view introduced in recent works where the exterior derivative of the Killing…
Massive tensor multiplets have recently been scrutinized in hep-th/0410051 and hep-th/0410149, as they appear in orientifold compactifications of type IIB string theory. Here we formulate several dually equivalent models for massive N = 1,…
We briefly discuss an algorithm for the tensor reduction of the two-loop massless crossed boxes, with light-like external legs, and the computation of the relative master integrals.
We introduce an algorithm to decide isomorphism between tensors. The algorithm uses the Lie algebra of derivations of a tensor to compress the space in which the search takes place to a so-called densor space. To make the method practicable…
When spacetime torsion is present, geodesics and autoparallels generically do not coincide. In this work, the well-known method that uses Killing vectors to solve the geodesic equations is generalized for autoparallels. The main definition…