Direct sum of connections
Further information: Direct sum of connections is associative upto natural isomorphism
Further information: Direct sum of connections is commutative upto natural isomorphism
Distributivity relation with tensor product
Further information: Distributivity relation between direct sum and tensor product of connections
Suppose are vector bundles over a differential manifold , with connections respectively. Then, under the natural isomorphism:
we have an identification between and . Here, is the direct sum of connections.
An analogous distributivity law identifies and .
Commutes with dual connection operation
Further information: Direct sum of dual connections equals dual connection to direct sum