Symmetric Killing tensors on almost abelian Lie groups
Differential Geometry
2025-10-01 v1
Abstract
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 the sense that they can be expressed as a polynomial in the Killing vector fields and the Riemannian metric.
Keywords
Cite
@article{arxiv.2509.26195,
title = {Symmetric Killing tensors on almost abelian Lie groups},
author = {Renan Berto-Cuevas and Viviana del Barco and Andrei Moroianu},
journal= {arXiv preprint arXiv:2509.26195},
year = {2025}
}