Sierra, José M.Valdés Morales, Antonio2023-06-202023-06-2019970011-464210.1023/A:1022440104951https://hdl.handle.net/20.500.14352/58671Let P be a G-structure on a manifold M and AdP be the adjoint bundle of P. The authors deduce the following main result: there exists a unique connection r adapted to P such that trace(S iX Tor(r)) = 0 for every section S of AdP and every vector field X on M, provided Tor(r) stands for the torsion tensor field of r. Two examples, namely almost Hermitian structures and almost contact metric structures, are discussed in more detail. Another interesting result reads: for a given structure group G, if it is possible to attach a connection to each G-structure in a functorial way with the additional assumption that the connection depends on first order contact only, then the first prolongation of the Lie algebra of G vanishesengjournal articlehttp://link.springer.com/content/pdf/10.1023%2FA%3A1022440104951.pdfhttp://link.springer.comopen access514.7G-structureconnectionnatural connectiontorsionGeometría diferencial1204.04 Geometría Diferencial