  For a general affine connection with parallel torsion and curvature, we show
that a post-Lie algebra structure exists on its space of vector fields,
generalizing previous results for flat connections. However, for non-flat
connections, the vector fields alone are not enough, as the presence of
curvature also necessitates that we include endomorphisms corresponding to
infinitesimal actions of the holonomy group. We give details on the universal
Lie algebra of this post-Lie algebra and give applications for solving
differential equations on manifolds.
