# Difference between revisions of "Tensor product of metric connections is metric"

From Diffgeom

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* [[Tensor product of flat connections is flat]] | * [[Tensor product of flat connections is flat]] |

## Revision as of 21:30, 24 July 2009

## Statement

A differential manifold . Two metric bundles and (i.e., are vector bundles and are Riemannian metrics or pseudo-Riemannian metrics on these). are metric connections on and respectively. Then, the tensor product of connections is a metric connection on .