Related papers: Killing Tensors from Conformal Killing Vectors
Symmetric conformal Killing tensors and (skew-symmetric) conformal Yano-Killing tensors for Euclidean Taub-NUT metric are given in explicit form. Relations between Yano and CYK tensors in terms of conformal rescaling are discussed.
We prove that every conformal vector field on the complex hyperbolic space $\mathbb{C}H^n$ is Killing for all $n\ge 2$. Although this rigidity is classically known, our proof is entirely different in nature: it is local, analytic, and fully…
Liouville integrable separable systems with quadratic in momenta first integrals are considered. Particular attention is paid to the systems generated by the so-called special conformal Killing tensors, i.e. Benenti systems. Then,…
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…
In this article, I discuss the construction of some globally conserved currents that one can construct in the absence of a Killing vector. One is based on the Komar current, which is constructed from an arbitrary vector field and has an…
Valence two Killing tensors in the Euclidean and Minkowski planes are classified under the action of the group which preserves the type of the corresponding Killing web. The classification is based on an analysis of the system of…
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 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 investigate Killing tensors for various black hole solutions of supergravity theories. Rotating black holes of an ungauged theory, toroidally compactified heterotic supergravity, with NUT parameters and two U(1) gauge fields are…
We study the integrability conditions of the conformal Killing equations for the Eisenhart lift of a scalar field in a flat Friedmann-Lema\^\i tre-Robertson-Walker universe. We show that the potential found in our earlier work is already…
The Newman-Penrose equations for spacetimes having one spacelike Killing vector are reduced -- in a geometrically defined "canonical frame'' -- to a minimal set, and its differential structure is studied. Expressions for the frame vectors…
We show the existence of conformal Killing-Yano tensors on a manifold endowed with a mixed 3-Sasakian structure.
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…
We first show how, from the general 3rd order ODE of the form z'''=F(z,z',z'',s), one can construct a natural Lorentzian conformal metric on the four-dimensional space (z,z',z'',s). When the function F(z,z',z'',s) satisfies a special…
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…
A characterization of the Kerr-NUT-(A)de Sitter metric among four dimensional \Lambda-vacuum spacetimes admitting a Killing vector is obtained in terms of the proportionality of the self-dual Weyl tensor and a natural self-dual double…
We give a classification for connected complete locally irreducible Riemannian manifolds with nonpositive curvature operator, which admit a nonzero closed or co-closed conformal Killing $L^{2}-$form. Moreover, we prove vanishing theorems…
(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.
A definition is suggested for affine symmetry tensors, which generalize the notion of affine vectors in the same way that (conformal) Killing tensors generalize (conformal) Killing vectors. An identity for these tensors is proved, which…
We construct a family of finite element sub-complexes of the conformal complex on tetrahedral meshes and show their exactness on contractible domains. This complex includes vector fields and symmetric and traceless tensor fields, connected…