A Calabi operator for Riemannian locally symmetric spaces
Abstract
On a Riemannian manifold of constant curvature, the Calabi operator is a second order linear differential operator that provides local integrability conditions for the range of the Killing operator. We generalise this operator to provide linear second order local integrability conditions on Riemannian locally symmetric spaces, whenever this is possible. Specifically, we show that this generalised operator always works in the irreducible case and we identify precisely those products for which it fails.
Keywords
Cite
@article{arxiv.2112.00841,
title = {A Calabi operator for Riemannian locally symmetric spaces},
author = {Federico Costanza and Michael Eastwood and Thomas Leistner and Benjamin McMillan},
journal= {arXiv preprint arXiv:2112.00841},
year = {2024}
}
Comments
17 pages. A spelling mistake has been corrected. Our proof of Proposition 5 has been improved. A missing curvature term has been added to (31): it does not effect the subsequent argument. Several improvements have been made. We now avoid using the Ambrose-Singer holonomy theorem