Cartan Geometries and their Symmetries - A Lie Algebroid Approach (Hardcover, 1st ed. 2016)

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.

General

Imprint:	Atlantis Press (Zeger Karssen)
Country of origin:	Netherlands
Series:	Atlantis Studies in Variational Geometry, 4
Release date:	June 2016
First published:	2016
Authors:	Mike Crampin • David Saunders
Dimensions:	235 x 155 x 19mm (L x W x T)
Format:	Hardcover
Pages:	290
Edition:	1st ed. 2016
ISBN-13:	978-9462391918
Categories:	Books > Science & Mathematics > Mathematics > Geometry > Differential & Riemannian geometry
LSN:	9462391912
Barcode:	9789462391918

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