Connections on Vector Bundles

Abstract

We note that symbols x ¹,..., x ^m denote not only a part of the local coordinates in formula (17) in Chap. 34 in the chart (ε _Uα , g _α ) but also the local coordinates in the chart (U _α , h _α ) of the manifold β. Because of this convention, which does not lead to confusion if we are sufficiently careful, the projection π is written in local coordinates by the tautological relations

$${x^k} = {x^k},\,k = 1,...,m.$$