Year: 2024
Type: article
Abstract: We prove that on the product of two Riemannian manifolds one of which is compact, any Killing tensor is reducible, that is, is the sum of products of Killing tensors on the factors. The same is true for the lifts to the universal cover of Killing tensors on a compact manifold with reducible holonomy. We give a local description of Killing tensors on product manifolds and present an example of a complete product manifold whose factors are locally irreducible which admits an irreducible Killing tensor field.
Source: manuscripta mathematica
Authors: Vladimir S. Matveev, Yuri Nikolayevsky
Institutions: Friedrich Schiller University Jena, La Trobe University
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,990
OpenAlex ID: W4405233761