The range of a connection and a Calabi operator for Lorentzian locally symmetric spaces

Autor:	Costanza, Federico, Eastwood, Michael, Leistner, Thomas, McMillan, Benjamin
Rok vydání:	2023
Předmět:	Mathematics - Differential Geometry 53C35 (Primary) 53B30 53B05 53A20 (Secondary)
Druh dokumentu:	Working Paper
Popis:	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. Comment: 25 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2302.04480 Zobrazit plný text záznamu View this record from Arxiv