Difference between revisions of "Dual connection to flat connection is flat"
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Latest revision as of 22:15, 24 July 2009
Contents
Statement
Statement in the language of connections
Suppose is a differential manifold, is a vector bundle over , and is a connection on . Suppose is the dual bundle to and is the dual connection to .
Then, if is a flat connection (i.e., the Riemann curvature tensor is identically zero), is also a flat connection.
Statement in the language of modules over the connection algebra
Fill this in later