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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Calvaruso, G., Castrillón López, M. (2019). G-structures, Holonomy and Homogeneous Spaces. In: Pseudo-Riemannian Homogeneous Structures. Developments in Mathematics, vol 59. Springer, Cham. https://doi.org/10.1007/978-3-030-18152-9_1
Download citation
DOI: https://doi.org/10.1007/978-3-030-18152-9_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-18151-2
Online ISBN: 978-3-030-18152-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)