In view of applications to Kaluza-Klein theories in a new affine framework, we investigate natural decompositions of linear connections in U(1)-bundles. Under a regularity condition, amounting to require that covariant derivatives of vertical vectorfields along vertical vectorfields are totally vertical, we show that a linear connection projects uniquely onto a principal connection. The relations with the metric case are also discussed.
A natural decomposition of S1-invariant linear connections on S1-bundles
FERRARIS, Marco;FRANCAVIGLIA, Mauro
1988-01-01
Abstract
In view of applications to Kaluza-Klein theories in a new affine framework, we investigate natural decompositions of linear connections in U(1)-bundles. Under a regularity condition, amounting to require that covariant derivatives of vertical vectorfields along vertical vectorfields are totally vertical, we show that a linear connection projects uniquely onto a principal connection. The relations with the metric case are also discussed.
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