Affine space of connections

From Diffgeom

This article defines a basic construct that makes sense on any differential manifold
View a complete list of basic constructs on differential manifolds

Definition

Given a differential manifold and a vector bundle over , the affine space of connections on is defined as the set of all connections on , viewed as a subset of the vector space of all bilinear maps:

This subset is in fact an affine space, because the condition of being a difference of two connections is a linear system of conditions. Fill this in later