Curvature

Abstract

We consider in this Chapter the notion of “curvature”, which, under supplementary suitable assumptions for a given differential triad, can be associated, in a natural way, with any given A-connection. Thus, in complete contrast with the situation one encounters with the case of A-connections, which, as we know already (cf. Chapter VI in the preceding), do not always exist, we realize here that an A-connection in the case there does exist is, instead, always accompanied with a curvature. This fact, as we shall see later on (cf. thus Chapter X in the sequel), can acquire an appropriate physical interpretation, as well. Yet, as was the case hitherto, one still witnesses here that several fundamental notions and results of the classical theory can also be recasted within the present abstract (axiomatic) framework, that has been advocated so far by this study.