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G-structures, Holonomy and Homogeneous Spaces

  • Giovanni CalvarusoEmail author
  • Marco Castrillón López
Chapter
Part of the Developments in Mathematics book series (DEVM, volume 59)

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.

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Dipartimento di Matematica e Fisica “Ennio De Giorgi”Università del SalentoLecceItaly
  2. 2.Facultad de Ciencias MatemáticasUniversidad Complutense de MadridMadridSpain

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