Sierra, José M.Valdés Morales, Antonio2023-06-202023-06-201997M.F. Atiyah, R. Bott, V. K. Patodi: On the heat equation and the index theorem. Inventiones Math. 19 (1973), 279-230. D.E. Blair: Contact manifolds in Riemannian geometry. Lecture Notes in Math., vol 509. Springer, Berlin, 1976. A. Ferrández, V. Miquel,: Hermitian natural tensors. Math. Scand. 64 (1989), 233-250. P. B. Gilkey: Local invariants of a pseudo-Riemannian manifold. Math. Scand. 36 (1975), 109-130. Victor Guillemin: The integrability problem for G-structures. Trans. Amer. Math. Soc. 116 (1965), 544-560. S. Kobayashi and K. Nomizu: Foundations of Differential Geometry I and II. Wiley, New York, 1963 and 1969. I. Kolár, P. Michor and J. Slovak: Natural Operations in Differential Geometry. Springer-Verlag, Berlin, 1993. A. Valdés: Invariantes diferenciales del fibrado de las referencias proyectivas de una variedad diferenciable y el problema de equivalencia de E. Cartan asociado. Ph. D. Dissertation, Universidad Complutense de Madrid. 1994. A. Valdés: Differential invariants of R*-structures. Math. Proc. Camb. Phil. Soc. 119 (1996), 341-356.0011-464210.1023/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