necessary to consider the second bundle. The curvature form of our connection is a tensorial quadratic differential form in
, of type
and with values in the Lie algebra
of
. Since the Lie algebra
of
is a subalgebra of
, there is a natural projection of
into the quotient space
. The image of the curvature form under this projection will be called the torsion form or the torsion tensor. If the forms
in (13) define a
-connection, the vanishing of the torsion form is expressed analytically by the conditions
We proceed to derive the analytical formulas for the theory of a
By taking the exterior derivative of (23) and using (18), we get
where we put
For a fixed value of
getting
or
Since the infinitesimal transformations
are linearly independent, this implies that
It follows that
where
It follows that
Since
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