Cartan Geometries and their Symmetries is popular PDF and ePub book, written by Mike Crampin in 2016-05-20, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Cartan Geometries and their Symmetries can be Read Online from any device for your convenience.
Cartan Geometries and their Symmetries Book PDF Summary
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.
Detail Book of Cartan Geometries and their Symmetries PDF
- Author : Mike Crampin
- Release : 20 May 2016
- Publisher : Springer
- ISBN : 9789462391925
- Genre : Mathematics
- Total Page : 298 pages
- Language : English
- PDF File Size : 10,7 Mb
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