Difference between revisions of "Dual connection"
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(New page: ==Definition== Suppose <math>E</math> is a vector bundle over a differential manifold <math>M</math> and <math>\nabla</math> is a connection on <math>E</math>. The '''dual con...) |
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Latest revision as of 19:39, 18 May 2008
Definition
Suppose 
is a vector bundle over a differential manifold 
and 
is a connection on . The dual connection to , denoted 
, is a connection on the dual vector bundle 
, defined as follows.
For any 
and 
, we have:
where 
Motivation
The definition of a dual connection is chosen in such a way that the bilinear form for evaluation:
satisfies the Leibniz rule. In other wors, we need to ensure that for 
and , we have:
