Killing vector fields and the holonomy algebra in semiriemannian manifolds (Q909267)

A well-known theorem of B. Kostant states that in case of compact Riemannian manifolds the operator \(A_ X:=L_ X-\nabla_ X\) lies in the holonomy algebra of the manifold. In this paper the author generalizes this result to compact semi-Riemannian manifolds. He also proves that on a compact homogeneous flat semi-Riemannian manifold any Killing vector field is parallel.