Abstract
The generators of Killing vector and tensor geodesic conservation laws are derived. It is shown that the generator of a Killing vector conservation law coincides with the Killing field itself. For Killing tensors the generators are not space-time vector fields but rather depend on the geodesic tangent vector and therefore lie in a jet space of the geodesic equations. By regarding the metric as a field on the one-jet space of the geodesic equations, the action of the Killing tensor generators on the metric can be defined in a natural way. It is found that the metric is not invariant under Killing tensor symmetries. This happens because the Killing tensor symmetries, unlike the Killing vector symmetries, are divergence symmetries.
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