Rational First Integrals and Relative Killing Tensors

2024/12/05 by Boris Kruglikov, Kruglikov, Boris
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Differential Geometry (math.DG) #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2412.04151

openalex publication_date 2024/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We relate rational integrals of the geodesic flow of a (pseudo-)Riemannian metric to relative Killig tensors, describe the spaces they span and discuss upper bounds on their dimensions.

Related

• Killing tensors in spaces of constant curvature
• Killing tensor fields of third rank on a two-dimensional Riemannian torus
• Killing tensor fields on the 2-torus
• Geodesic normal coordinates and natural tensors for pseudo-Riemannian submanifolds
• Pseudo-Riemannian metrics on closed surfaces whose geodesic flows admit nontrivial integrals quadratic in momenta