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

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(Created page with '==Statement== A differential manifold <math>M</math>. Two fact about::metric bundles <math>(E,g)</math> and <math>(E',g')</math> (i.e., <math>E,E'</math> are [[vector bu…')
 
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==Related facts==
 
==Related facts==
  
* [[Tensor product of torsion-free connections is torsion-free]]
 
 
* [[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 M. Two metric bundles (E,g) and (E',g') (i.e., E,E' are vector bundles and g,g' are Riemannian metrics or pseudo-Riemannian metrics on these). \nabla, \nabla' are metric connections on (E,g) and (E',g') respectively. Then, the tensor product of connections \nabla \otimes \nabla' is a metric connection on (E \otimes E',g \otimes g').

Related facts