A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Researchers found indecomposable Killing tensor fields on quaternionic projective spaces.
The paper classifies Killing tensor fields on Riemannian symmetric spaces.
Killing tensors on complex projective space are identified and generated by Killing fields.
A symmetric tensor field on a Riemannian manifold is called Killing field if the symmetric part of its covariant derivative is equal to zero. There is a one to one correspondence between Killing tensor fields and first integrals of the geodesic flow which depend polynomially on the velocity. Therefore Killing tensor fi…
Researchers found non-Killing tensor fields on certain symmetric spaces.
Quadratic Killing tensors on Lie groups are always decomposable.
Stationary and axially symmetric space-times play an important role in astrophysics, particularly in the theory of neutron stars and black holes. The static vacuum sub-class of these space-times is known as Weyl's class, and contains the Schwarzschild space-time as its most prominent example. This paper is going to stu…
A vector field on a Riemannian manifold is called conformal Killing if it generates one-parameter group of conformal transformations. The class of conformal Killing symmetric tensor fields of an arbitrary rank is a natural generalization of the class of conformal Killing vector fields, and appears in different geometri…
Systematic prolongation for Killing two-tensors in symmetric spaces.
Killing tensors on reducible spaces are reducible, except for special cases.
Characterizes symmetric Killing tensors on specific Lie groups.
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 conformal Killing -tensors on Riemannian products of compact manifolds, Weitzenb…
The study finds conditions for a third rank Killing tensor field on a 2D Riemannian torus.
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 of Killing vector fields.
This paper is concerned with deformations of Kundt metrics in the direction of type tensors and nil-Killing vector fields whose flows give rise to such deformations. We find various characterizations within the Kundt class in terms of nil-Killing vector fields and obtain a theorem classifying algebraic stability …
New tensors help solve magnetic flow integrability.
Study on Haantjes tensors for superintegrable systems, focusing on vanishing properties.
We show that Killing tensors on conformally flat -dimensional tori whose conformal factor only depends on one variable, are polynomials in the metric and in the Killing vector fields. In other words, every first integral of the geodesic flow polynomial in the momenta on the sphere bundle of such a torus is linear in…
In the differential geometry of certain F-structures, the role of W-curvature tensor is very well known. A detailed study of this tensor has been made on the spacetime of general relativity. The spacetimes satisfying Einstein field equations with vanishing W-tensor have been considered and the existence of Killing and …
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 formulated as geodesic problems in curved spaces and spacetimes, and thus solving the de…
Study on type-D Ricci-flat metrics with Killing spinors and Killing vectors.
On a Hermitian manifold we construct a symmetric - tensor using the torsion and the curvature of the Chern connection. On a compact balanced Hermitian manifold we find necessary and sufficient conditions in terms of the tensor for a harmonic -form to be analytic and for an analytic -form to be harm…
New approach classifies conformal Killing vector fields for FLRW space-time.
We construct exact solutions of the Einstein-Dirac equation, which couples the gravitational field with an eigenspinor of the Dirac operator via the energy-momentum tensor. For this purpose we introduce a new field equation generalizing the notion of Killing spinors. The solutions of this spinorial field equation are c…
We study Finsler spacetimes and Killing vector fields taking care of the fact that the generalized metric tensor associated to the Lorentz-Finsler function is in general well defined only on a subset of the slit tangent bundle. We then introduce a new class of Finsler spacetimes endowed with a timelike Killing vect…
This article attempts to delineate the roles played by non-dynamical background structures and Killing symmetries in the construction of stress-energy-momentum tensors generated from a diffeomorphism invariant action density. An intrinsic coordinate independent approach puts into perspective a number of spurious argume…
Starting with the most general four-dimensional spacetime possessing two commuting Killing vectors and a nontrivial Killing tensor, we analytically integrate Einstein-Yang-Mills equations for a completely arbitrary gauge group. It is assumed that the gauge field inherits the symmetries of the background and is aligned …
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 existence of a Killing-Yano tensor are also obtained. By means of such conditions, it is…
The article discusses conservation laws for polyharmonic maps and their applications.
We construct an algebra of nonlinear generalized tensor fields on manifolds in the sense of J.-F. Colombeau, i.e., containing distributional tensor fields as a linear subspace and smooth tensor fields as a faithful subalgebra. The use of a background connection on the manifold allows for a simplified construction based…
We review properties of so-called special conformal Killing tensors on a Riemannian manifold and the way they give rise to a Poisson-Nijenhuis structure on the tangent bundle . We then address the question of generalizing this concept to a Finsler space, where the metric tensor field comes from a regular La…
Classifies 3-manifolds with Killing vector fields, extending results from Riemannian to Lorentzian.
The paper introduces and characterizes almost ω-Bach solitons on various product manifolds.
The paper explores conditions for homothetic Killing vectors on spacetime hypersurfaces.
New concept of metric Lie algebras helps classify Lie groups.
New currents derived from Killing-Yano tensors for gravity.
Upper bound found for divergence-free Killing 2-tensors on manifolds.
Characterizes conformal Killing tensors and their Killing scales.
Study on type-D metrics aligned with Einstein-Maxwell equations, deriving solutions.
The paper classifies tensors on specific Lorentzian metrics.
The properties of a Killing-Yano tensor of order n-1 in an n-dimensional manifold are investigated. The integrability conditions are worked out and all metrics admitting a Killing-Yano tensor of order n-1 are found. It is pointed out a connection between such tensors and a generalization of the concept of angular momen…
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 Nijenhuis integrability conditions for a Killing tensor into purely algebraic integra…
Study transverse metric expansion on null hypersurfaces, proving uniqueness for Killing horizons.
Relates geodesic integrals to Killing tensors, exploring their dimensions.
In this brief survey, we will remark the interaction among the Hessian tensor on a semi-Riemannian manifold and some of the several questions in Lorentzian (and also in semi-Riemannian) geometry where this 2-covariant tensor is involved. In particular, we deal with the characterization of Killing vector fields and the …
The integrability conditions for the existence of Killing-Yano tensors or, equivalently, covariantly closed conformal Killing-Yano tensors, in the presence of torsion are worked out. As an application, all metrics and torsions compatible with the existence of a Killing-Yano tensor of order n-1 are obtained. Finally, th…
In this note, we introduce a new type of warped products called as sequential warped products to cover a wider variety of exact solutions to Einstein's equation. First, we study the geometry of sequential warped products and obtain covariant derivatives, curvature tensor, Ricci curvature and scalar curvature formulas. …
The article studies spinor and tensor fields on curved spaces, deriving formulas and spectra.