A Calabi operator for Riemannian locally symmetric spaces
Abstract
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.
Fields of Study & Subjects
Advanced Algebra and Geometry
Geometric Analysis and Curvature Flows
Geometry and complex manifolds
Publication details
- Journal / source
- American Journal of Mathematics
- Publisher
- Project MUSE
- Volume
- 148
- Issue
- 4
- Pages
- 1003–1028
- Publication date
- 1 August 2026
- Language
- EN