# A Calabi operator for Riemannian locally symmetric spaces

@inproceedings{Costanza2021ACO, title={A Calabi operator for Riemannian locally symmetric spaces}, author={Federico Costanza and Michael Eastwood and Thomas Leistner and Ben Mcmillan}, year={2021} }

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…

## One Citation

### The linearised Einstein equations as a gauge theory

- Physics, Mathematics
- 2022

. We linearise the Einstein vacuum equations with a cosmological constant via the Calabi operator from projective diﬀerential geometry.

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