Related papers: Killing tensors on tori
The solutions of generalized Killing equation have been obtained for line element with initial $t^2 \oplus so(3)$ symmetry. The coefficients of the metric $g$ corresponding to these vector fields are written down.
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…
The classification of conformal Killing vector fields for FLRW space-time from Riemannian point of view was done by Maartens-Maharaj in \cite{Maartens1986}. In this paper, we introduce conformal Killing vector fields from a new point of…
We classify the supersymmetric solutions of minimal $N=2$ gauged supergravity in four dimensions with neutral signature. They are distinguished according to the sign of the cosmological constant and whether the vector field constructed as a…
In this paper we have obtained evolution of some geometric quantities on a compact Riemannian manifold $M^n$ when the metric is a Yamabe soliton. Using these quantities we have obtained bound on the soliton constant. We have proved that the…
We study metric solutions of Einstein-anti-Maxwell theory admitting Killing spinors. The analogue of the IWP metric which admits a space-like Killing vector is found and is expressed in terms of a complex function satisfying the wave…
We provide a general method for studying manifestly $O(n+1)$ covariant formulation of $p$-form gauge theories by stereographically projecting these theories, defined in flat Euclidean space, onto the surface of a hypersphere. The gauge…
Killing vector fields $K$ are defined on Finsler manifold. The Killing symmetry is reformulated simply as $\delta K^\flat =0$ by using the Killing non-linear 1-form $K^\flat$ and the spray operator $\delta$ with the Finsler non-linear…
We devise an algorithm which allows one to count the number of Killing vectors for a Lorentzian manifold of dimension 3. Our algorithm relies on the principal traces of powers of the Ricci tensor and branches intricately according to the…
We employ the language of Cartan's geometry to present a model for studying vector spaces of Killing two-tensors defined in pseudo-Riemannian spaces of constant curvature under the action of the corresponding isometry group. We also discuss…
Given an d-dimensional manifold with two commuting Killing vectors, together with an d - 1 dimensional submanifold in which one of the Killing vectors lies, then the lapse and shift of the second Killing vector, relative to this slice,…
Let $(M,F)$ be a compact connected homogeneous non-Riemannian Finsler manifold with $\dim M>1$. We prove that any conformal vector field on $(M,F)$ is a Killing vector field. Further more, we prove that $\rho F$ is a homogeneous Finsler…
New geometries were obtained by adding a suitable surface term involving the components of the angular momentum to the corresponding free Lagrangians. Killing vectors, Killing-Yano and Killing tensors of the obtained manifolds were…
Many extensions of General Relativity are based on considering metric and affine structures as independent properties of spacetime. This leads to the possibility of introducing torsion as an independent degree of freedom. In this article we…
Killing tensor fields have been thought of as describing hidden symmetry of space(-time) since they are in one-to-one correspondence with polynomial first integrals of geodesic equations. Many problems in classical mechanics can be…
As we have proved in [L], the geodesic flows associated with the flat metrics on T^2 minimize the polynomial entropy. In this paper, we show that, among the geodesic flows that are Bott integrable and dynamically coherent, the geodesic…
In this note we give a criterion for the existence of a fractional-linear integral for a geodesic flow on a Riemannian surface and explain that modulo M\"obius transformations the moduli space of such local integrals (if nonempty) is either…
We reformulate the abelian tensor multiplet on a curved spacetime with at least two supercharges in a cohomological form where all the bosonic and fermionic fields become tensor fields. These tensor fields are rewritten as fields in loop…
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,…
We formulate several criteria under which the symmetries associated with the Killing and Killing-Yano tensors on the base space can be lifted to the symmetries of the full warped geometry. The procedure is explicitly illustrated on several…