The range of a connection and a Calabi operator for Lorentzian locally symmetric spaces
Date
2025
Authors
Costanza, F.
Eastwood, M.
Leistner, T.
McMillan, B.
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Journal article
Citation
Asian Journal of Mathematics, 2025; 29(2):171-200
Statement of Responsibility
Federico Costanza, Michael Eastwood, Thomas Leistner and Thomas Leistner
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Abstract
For semi-Riemannian manifolds of constant sectional curvature, the Calabi operator is a second order linear differential operator that provides local integrability conditions for the range of the Killing operator. In this article, extending earlier results in the Riemannian setting, we identify the Lorentzian locally symmetric spaces on which the Calabi operator is sufficient to identify the range of the Killing operator. Specifically, this is always the case for indecomposable spaces and we identify precisely those products for which it fails. Our method is quite general in that we firstly develop criteria to be in the range of a connection, viewed as a linear differential operator. Then we ascertain how these criteria apply in the case of what we call the Killing connection.
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Published 17 July 2025
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