Motivated by physical applications, we revisit some familiar concepts in principal $G$-bundles by means of right-invariant bases of vector fields. In particular, we show that the use of these bases (which, in contrast to the left-invariant ones, are generally not global) allows one to deal more easily with explicit calculations involving $G$-invariant linear connections and tensors.
Remarks on right-invariant vectorfield bases in principal bundles and their applications to decomposition theorems
FERRARIS, Marco;FRANCAVIGLIA, Mauro
1988-01-01
Abstract
Motivated by physical applications, we revisit some familiar concepts in principal $G$-bundles by means of right-invariant bases of vector fields. In particular, we show that the use of these bases (which, in contrast to the left-invariant ones, are generally not global) allows one to deal more easily with explicit calculations involving $G$-invariant linear connections and tensors.
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