In this work we study the relationship between affine connections and distributions. In particular, given an affine connection and a distribution, we construct a family of affine connections which restrict to a vector bundle connection in the distribution. The difference between each of the derived connections and the original connection may be thought of as a natural generalisation of the affine second fundamental form for submanifolds. Of some interest is the determination of those infinitesimal symmetries for the original connection which are also infinitesimal symmetries for the new affine connection. Some examples illustrate the theory.
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