Dual connection to flat connection is flat
From Diffgeom
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