G-structures, Holonomy and Homogeneous Spaces

Abstract

In the following sections we establish the foundations needed for the subsequent chapters. The reader is assumed to be familiar with the notions of smooth manifolds, tensorial algebra, pseudo-Riemannian geometry, Lie groups and actions of groups. From this starting point, we introduce principal bundles and connections, with special emphasis on the frame bundle and its reductions, that is, the so-called G-structures. The horizontal lift of paths in principal bundles with respect to a connection leads to the notion of holonomy, which is essential throughout this book.