Quadratic Killing tensors on symmetric spaces which are not generated by Killing vector fields
Year: 2024
Type: article
Abstract: Every Killing tensor field on the space of constant curvature and on the complex projective space can be decomposed into the sum of symmetric tensor products of Killing vector fields (equivalently, every polynomial in velocities integral of the geodesic flow is a polynomial in the linear integrals). This fact led to the natural question on whether this property is shared by Killing tensor fields on all Riemannian symmetric spaces. We answer this question in the negative by constructing explicit examples of quadratic Killing tensor fields which are not quadratic forms in the Killing vector fields on the quaternionic projective spaces ℍ P n , n ≥ 3 , and on the Cayley projective plane 𝕆 P 2 .
Source: Comptes Rendus Mathématique
DOI: 10.5802/crmath.624
Authors: Vladimir S. Matveev, Yuri Nikolayevsky
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4404045128