\(A_ X\)-operator on complete Riemannian manifolds (Q1081845)

In a Riemannian manifold (M,g), let \(L_ X\) and \(\nabla_ X\) be the Lie and covariant derivations with respect to a Killing vector field X. Then \(A_ X=L_ X-\nabla_ X\) is a skew-symmetric operator field. B. Kostant proved that \(A_ X\) belongs to the holonomy algebra at each point, if M is compact. The present author proves that this fact is also true in a complete non-compact (M,g), under the assumption that X has a finite global norm.