arXiv subjects

Wijnand Steneker

Publications and source records attributed to Wijnand Steneker.

5 recordsLinked to original sources

arXiv2026

Differential Invariants of Carrollian Spacetimes

We compute invariants of Carrollian spacetimes, deriving them from the geometry of the screen bundle. For generic Carrollian structures we specify how to generate the entire algebra of differential invariants, with emphasis on dimension 3, which has special physical relevance. Then, in the framework of jet-spaces, we compute the numerology behind these invariants: the Hilbert and Poincaré functions that govern their numbers according to order. Finally, we compute the Spencer cohomology behind the Carrollian geometry that, in particular, contains the spaces of intrinsic torsion and intrinsic curvature, which are fundamental invariants, important in the equivalence problem and symmetry analysis. Thus, we also discuss symmetry sizes of Carrollian spacetimes.

math.DG↗

arXiv2026

Jet-Density of Finite-Gap Solutions for Classes of BKM Systems

We show that jets of initial data can be approximated up to arbitrary order by finite-gap solutions for classes of so-called BKM systems of PDEs introduced by Bolsinov--Konyaev--Matveev, which include classical PDEs such as KdV, Kaup--Boussinesq and Camassa--Holm. Finite-gap solutions are obtained via a finite-reduction map, defined algebraically, which sends solutions of a Stäckel system to solutions of the BKM PDE. For the classes containing KdV and Kaup--Boussinesq we obtain full jet-surjectivity via a triangular structure, whereas for the class containing Camassa--Holm we establish jet-surjectivity on an open set of initial data over $\mathbb{R}$ and a Zariski-open (dense) set over $\mathbb{C}$.

math.AP↗

arXiv2026

On globally invariant Euler--Lagrange equations for curves

Invariant Lagrangians yield invariant Euler-Lagrange equations, and it was discussed in the literature how to compute those using various local methods. The focus of this paper is on global algebraic differential invariants. In this case the computation can be modified in several aspects. We will discuss relations with previous approaches and some foundational aspects. The theory of invariant Euler-Lagrange equations was applied to curves with respect to the motion group in the Euclidean plane and space. We expand those computations to the next dimension four (Minkowski spacetime), which already exhibits computational challenges. We also provide formulas for other examples, namely the projective and conformal (Möbius) groups and relate to some recent applications.

math.DG↗

arXiv2025

Variationality of conformal geodesics in dimension 3

Conformal geodesics form an invariantly defined family of unparametrized curves in a conformal manifold generalizing unparametrized geodesics/paths of projective connections. The equation describing them is of third order, and it was an open problem whether they are given by an Euler--Lagrange equation. In dimension 3 (the simplest, but most important from the viewpoint of physical applications) we demonstrate that the equation for unparametrized conformal geodesics is variational.

math.DG↗

arXiv2022

Killing Tensors in Koutras-McIntosh Spacetimes

The Koutras-McIntosh family of metrics include conformally flat pp-waves and the Wils metric. It appeared in a paper of 1996 by Koutras-McIntosh as an example of a pure radiation spacetime without scalar curvature invariants or infinitesimal symmetries. Here we demonstrate that these metrics have no "hidden symmetries", by which we mean Killing tensors of low degrees. For the particular case of Wils metrics we show the nonexistence of Killing tensors up to degree 6. The technique we use is the geometric theory of overdetermined PDEs and the Cartan prolongation-projection method. Application of those allows to prove the nonexistence of polynomial in momenta integrals for the equation of geodesics in a mathematical rigorous way. Using the same technique we can completely classify all lower degree Killing tensors and, in particular, prove that for generic pp-waves all Killing tensors of degree 3 and 4 are reducible.

gr-qc↗