Authors:
- 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
- Includes supplementary material: sn.pub/extras
Part of the book series: Atlantis Studies in Variational Geometry (ASVG, volume 4)
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Table of contents (12 chapters)
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Front Matter
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Back Matter
About this book
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.
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Authors and Affiliations
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Burnham Market, United Kingdom
Mike Crampin
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University of Ostrava, Ostrava, Czech Republic
David Saunders
Bibliographic Information
Book Title: Cartan Geometries and their Symmetries
Book Subtitle: A Lie Algebroid Approach
Authors: Mike Crampin, David Saunders
Series Title: Atlantis Studies in Variational Geometry
DOI: https://doi.org/10.2991/978-94-6239-192-5
Publisher: Atlantis Press Paris
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Atlantis Press and the author(s) 2016
Hardcover ISBN: 978-94-6239-191-8Published: 30 May 2016
eBook ISBN: 978-94-6239-192-5Published: 20 May 2016
Series ISSN: 2214-0700
Series E-ISSN: 2214-0719
Edition Number: 1
Number of Pages: XIV, 290
Topics: Differential Geometry