= Affine space of vector-bundle connections
{title2=$\operatorname{Conn}(E)=\nabla^0+\Omega^1(M;\operatorname{End}E)$}
The difference of two <connections on a vector bundle> is a smooth one-form with values in the endomorphism bundle: the Leibniz derivative terms cancel, leaving pointwise linearity in both the tangent vector and section value. Conversely every such form added to a connection gives another connection. Thus the collection is an <affine space> with this model vector space. Choosing $\nabla^0$ supplies a noncanonical origin; there is no distinguished zero connection.
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