Post-Lie Algebra Structure of Manifolds with Constant Curvature and Torsion

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