The natural operators of general affine connections into general affine connections

Abstract

We reduce the problem of describing all $\mathcal{M} f_m$-natural operators  transforming general affine connections on $m$-manifolds into general affine ones to the known description of all $GL(\mathbf{R}^m)$-invariant maps $\mathbf{R}^{m*}\otimes \mathbf{R}^m\to \otimes^k\mathbf{R}^{m*}\otimes\otimes ^k\mathbf{R}^m$ for $k=1,3$.