相关论文: Geometrical classification of Killing tensors on b…
We employ an isometry group invariants approach to study Killing tensors of valence three defined in the Euclidean plane. The corresponding invariants are found to be homogeneous polynomials of the parameters of the vector space of the…
The systematic derivation of constants of the motion, based on Killing tensors and the gauge covariant approach, is outlined. Quantum dots are shown to support second-, third- and fourth-rank Killing tensors.
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…
This paper presents a classification of irreducible Killing and conformal Killing 2-tensors on homogeneous plane waves, a specific class of Lorentzian metrics on four-dimensional manifolds. Using the framework of BGG operators, we derive…
The second order Killing and conformal tensors are analyzed in terms of their spectral decomposition, and some properties of the eigenvalues and the eigenspaces are shown. When the tensor is of type I with only two different eigenvalues,…
Given a $n$-dimensional Riemannian manifold of arbitrary signature, we illustrate an algebraic method for constructing the coordinate webs separating the geodesic Hamilton-Jacobi equation by means of the eigenvalues of $m \leq n$ Killing…
We study left-invariant symmetric Killing 2-tensors on 2-step nilpotent Lie groups endowed with a left-invariant Riemannian metric, and construct genuine examples, which are not linear combinations of parallel tensors and symmetric products…
A Killing tensor field on a Riemannian space corresponds to an integral of the geodesic flow polynomial in momenta. A Killing tensor field is called decomposable if it is a polynomial in Killing vector fields. In this paper, we first prove…
An invariant characterization of the rotationally symmetric R-separable webs for the Laplace equation in Euclidean space is given in terms of invariants and covariants of a real binary quartic canonically associated to the characteristic…
We introduce an appropriate formalism in order to study conformal Killing (symmetric) tensors on Riemannian manifolds. We reprove in a simple way some known results in the field and obtain several new results, like the classification of…
A rank $m$ symmetric tensor field on a Riemannian manifold is called a Killing field if the symmetric part of its covariant derivative is equal to zero. Such a field determines the first integral of the geodesic flow which is a degree $m$…
In this paper the isometries of the dual space were investigated. The dual structural equations of a Killing tensor of order two were found . The flat space case was analyzed in details.
The invariant theory of Killing tensors (ITKT) is extended by introducing the new concepts of covariants and joint invariants of (product) vector spaces of Killing tensors defined in pseudo-Riemannian spaces of constant curvature. The…
We introduce the notion of metric Lie algebras of Killing type, which are characterized by the fact that all conformal Killing symmetric tensors are sums of Killing tensors and multiples of the metric tensor. We show that if a Lie algebra…
The aim of this paper is to classify compact, simply connected K\"ahler manifolds which admit J-invariant Killing tensor with two eigenvalues of multiplicity 2 and n-2 and with constant eigenvalue corresponding to 2-dimensional…
We use an isomorphism between the space of valence two Killing tensors on an n-dimensional constant sectional curvature manifold and the irreducible GL(n+1)-representation space of algebraic curvature tensors in order to translate the…
The Killing tensor equation is a first order differential equation on symmetric covariant tensors that generalises to higher rank the usual Killing vector equation on Riemannian manifolds. We view this more generally as an equation on any…
We present a purely geometric method for constructing a rank two Killing tensor in a spacetime with a codimension one foliation that lifts the trivial Killing tensors from slices to the entire manifold. The resulting Killing tensor can be…
In this work we provide a complete characterization of left-invariant symmetric Killing tensors on almost abelian Lie groups endowed with a left-invariant Riemannian metric. We show in particular that all such tensors are decomposable, in…
Benefiting from the index spinorial formalism, the Killing spinor equation is integrated in six-dimensional spacetimes. The integrability conditions for the existence of a Killing spinor are worked out and the Killing spinors are classified…