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Cartan Geometries and their Symmetries

Cartan Geometries and their Symmetries

A Lie Algebroid Approach

by David Saunders and Mike Crampin
Hardback
Publication Date: 21/05/2016
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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.
ISBN:
9789462391918
9789462391918
Category:
Differential & Riemannian geometry
Format:
Hardback
Publication Date:
21-05-2016
Publisher:
Atlantis Press (Zeger Karssen)
Country of origin:
Netherlands
Pages:
290
Dimensions (mm):
235x155x19mm
Weight:
5.8kg

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