Abstract
We give a generalization of the result obtained by C. Curras-Bosch. We consider the Av-operator associated to a transverse Killing fieldν on a complete foliated Riemannian manifold (M, ℱ, g). Under a certain assumption, we prove that, for eachx ∈M, (Av)x belongs to the Lie algebra of the linear holonomy group ψv(x). A special case of our result, the version of the foliation by points, implies the results given by B. Kostant (compact case) and C. Curras-Bosch (non-compact case).
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