Atlantis Studies in Variational Geometry

Cartan Geometries and their Symmetries

A Lie Algebroid Approach

Authors: Crampin, Mike, Saunders, David

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  • Expounds a new approach to the theory of Cartan connections as path connections on a certain class of Lie groupoids, or as infinitesimal connections on corresponding Lie algebroids
  • It contains a comprehensive account of the symmetries of Cartan geometries
  • Based on these ideas it extends Cartan's theory of a single ordinary differential equation to cover systems of such equations
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eBook 79,72 €
price for Spain (gross)
  • ISBN 978-94-6239-192-5
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Hardcover 98,79 €
price for Spain (gross)
  • ISBN 978-94-6239-191-8
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About this book

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, using Lie algebroids rather than Lie groupoids, and in particular using Lie algebroids of vector fields along the projection of the fibre bundle, may be of benefit.

We then introduce Cartan geometries, together with a number of tools we shall use to study them. We take, as particular examples, the four classical types of geometry: affine, projective, Riemannian and conformal geometry. We also see how our approach can start to fit into a more general theory. Finally, we specialize to the geometries (affine and projective) associated with path spaces and geodesics, and consider their symmetries and other properties.

Reviews

“The authors expose an alternative approach to Cartan geometries. … the book offers a nice exposition of the approach to Cartan geometries via Lie algebroids, one also has to say that, apart from the approach, the book remains in quite well-known territory.” (Andreas Cap, Mathematical Reviews, April 2017)

Table of contents (12 chapters)

Table of contents (12 chapters)

Buy this book

eBook 79,72 €
price for Spain (gross)
  • ISBN 978-94-6239-192-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 98,79 €
price for Spain (gross)
  • ISBN 978-94-6239-191-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Cartan Geometries and their Symmetries
Book Subtitle
A Lie Algebroid Approach
Authors
Series Title
Atlantis Studies in Variational Geometry
Series Volume
4
Copyright
2016
Publisher
Atlantis Press
Copyright Holder
Atlantis Press and the author(s)
eBook ISBN
978-94-6239-192-5
DOI
10.2991/978-94-6239-192-5
Hardcover ISBN
978-94-6239-191-8
Series ISSN
2214-0700
Edition Number
1
Number of Pages
XIV, 290
Topics