 Tensor product connection

ID: tensor-product-connection

Connections on

E

and

F

induce the connection on

E \otimes F

determined by

\nabla (s \otimes t) = (\nabla^{E} s) \otimes t + s \otimes (\nabla^{F} t) .

In tensor-product local frames its connection matrix is

A_{E} \otimes I + I \otimes A_{F}

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