Cartan Geometries and their Symmetries A Lie Algebroid Approach /

• Main Authors: Crampin, Mike (Author), Saunders, David (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Paris : Atlantis Press : Imprint: Atlantis Press, 2016.
• Series: Atlantis Studies in Variational Geometry, 4
• Subjects: Mathematics.; Differential geometry.; Differential Geometry.

In this book we first review the ideas of Lie groupoid and Lie algebroid, and the associated concepts of connection. We next consider Lie groupoids of fibre morphisms of a fibre bundle, and the connections on such groupoids together with their symmetries. We also see how the infinitesimal approach,...

Table of Contents:

• Lie groupoids and Lie algebroids
• Connections on Lie groupoids and Lie algebroids
• Groupoids of fibre morphisms
• Four case studies
• Symmetries
• Cartan geometries
• A comparison with alternative approaches
• Infinitesimal Cartan geometries on TM
• Projective geometry: the full version
• Conformal geometry: the full version
• Developments and geodesics
• Cartan theory of second-order differential equations. .