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Cartan geometries and their symmetri...

Crampin, Mike.

Cartan geometries and their symmetries[electronic resource] :a lie algebroid approach /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	512.55
書名/作者:	Cartan geometries and their symmetries : a lie algebroid approach // by Mike Crampin, David Saunders.
作者:	Crampin, Mike.
其他作者:	Saunders, David.
出版者:	Paris : : Atlantis Press :, 2016.
面頁冊數:	xiv, 290 p. : : ill., digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Lie algebroids.
標題:	Mathematics.
標題:	Differential Geometry.
ISBN:	9789462391925
ISBN:	9789462391918
摘要、提要註:	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.
電子資源:	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 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

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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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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650 1 4 $a Mathematics. $3 172349
650 2 4 $a Differential Geometry. $3 464898
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