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Cartan geometries and their symmetri...

Crampin, Mike.

Cartan geometries and their symmetriesa lie algebroid approach /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Cartan geometries and their symmetriesby Mike Crampin, David Saunders.
Reminder of title:	a lie algebroid approach /
Author:	Crampin, Mike.
other author:	Saunders, David.
Published:	Paris :Atlantis Press :2016.
Description:	xiv, 290 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Lie algebroids.
Online resource:	http://dx.doi.org/10.2991/978-94-6239-192-5
ISBN:	9789462391925$q(electronic bk.)

Cartan geometries and their symmetriesa lie algebroid approach /
Crampin, Mike.

Cartan geometries and their symmetriesa lie algebroid approach /[electronic resource] :by Mike Crampin, David Saunders. - Paris :Atlantis Press :2016. - xiv, 290 p. :ill., digital ;24 cm. - Atlantis studies in variational geometry,v.42214-0700 ;. - Atlantis studies in variational geometry ;v.1..

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: 9789462391925$q(electronic bk.)

Standard No.: 10.2991/978-94-6239-192-5doiSubjects--Topical Terms:

747939
Lie algebroids.

LC Class. No.: QA641

Dewey Class. No.: 512.55

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245 1 0 $a Cartan geometries and their symmetries $h [electronic resource] : $b a lie algebroid approach / $c by Mike Crampin, David Saunders.
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520 $a 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.
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