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Cartan geometries and their symmetri...
~
Crampin, Mike.
Cartan geometries and their symmetries[electronic resource] :a lie algebroid approach /
Record Type:
Language materials, printed : Monograph/item
[NT 15000414]:
512.55
Title/Author:
Cartan geometries and their symmetries : a lie algebroid approach // by Mike Crampin, David Saunders.
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.
Subject:
Mathematics.
Subject:
Differential Geometry.
ISBN:
9789462391925
ISBN:
9789462391918
[NT 15000229]:
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.
Online resource:
http://dx.doi.org/10.2991/978-94-6239-192-5
Cartan geometries and their symmetries[electronic resource] :a lie algebroid approach /
Crampin, Mike.
Cartan geometries and their symmetries
a 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
Standard No.: 10.2991/978-94-6239-192-5doiSubjects--Topical Terms:
647283
Lie algebroids.
LC Class. No.: QA641
Dewey Class. No.: 512.55
Cartan geometries and their symmetries[electronic resource] :a lie algebroid approach /
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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.
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Mathematics and Statistics (Springer-11649)
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