Currás Bosch, Carlos2009-04-062009-04-0619841088-6826https://hdl.handle.net/2445/7622We prove that for each Killing vector field $ X$ on a complete Riemannian manifold, whose orthogonal distribution is involutive, the $ (1,1)$ skew-symmetric operator $ {A_X}$ associated to $ X$ by $ {A_X} = {L_X} - {\nabla _X}$ lies in the holonomy algebra at each point. By using the same techniques, we also study when that operator lies in the infinitesimal and local holonomy algebras respectively.7 p.application/pdfeng(c) American Mathematical Society, 1984Camps vectorialsÀlgebraVector fieldsAlgebrainfo:eu-repo/semantics/article2623info:eu-repo/semantics/openAccess