\(A_{\nu}\)-operator on complete foliated Riemannian manifolds
Let F be an orientable differentiable foliation of the manifold M endowed with the complete Riemannian metric g which is F-bundle-like and F- minimizable. Let \(\nu\) be a transverse Killing field with finite global norm, and \((A_{\nu})_ x\), \(x\in M\), be the endomorphism associated to \(\nu\) by means of the covariant derivative. Then the author proves that \((A_{\nu})_ x\) belongs to the Lie algebra of the linear holonomy group of the transversal Riemannian connection of F at x. This generalizes a known theorem of Riemannian geometry.
scientific article; zbMATH DE number 4002974