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Cartan Geometries and their Symmetries = A Lie Algebroid Approach /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Cartan Geometries and their Symmetries/ by Mike Crampin, David Saunders.
其他題名:	A Lie Algebroid Approach /
作者:	Crampin, Mike.
其他作者:	Saunders, David.
面頁冊數:	XIV, 290 p.online resource. :
Contained By:	Springer Nature eBook
標題:	Differential geometry. -
電子資源:	https://doi.org/10.2991/978-94-6239-192-5
ISBN:	9789462391925

Cartan Geometries and their Symmetries = A Lie Algebroid Approach /
Crampin, Mike.

Cartan Geometries and their SymmetriesA Lie Algebroid Approach /[electronic resource] :by Mike Crampin, David Saunders. - 1st ed. 2016. - XIV, 290 p.online resource. - Atlantis Studies in Variational Geometry,42214-0700 ;. - Atlantis Studies in Variational Geometry,2.

Lie groupoids and Lie algebroids -- Connections on Lie groupoids and Lie algebroids -- Groupoids of ﬁbre morphisms -- Four case studies -- Symmetries -- Cartan geometries -- A comparison with alternative approaches -- Inﬁnitesimal Cartan geometries on TM -- Projective geometry: the full version -- Conformal geometry: the full version -- Developments and geodesics -- Cartan theory of second-order diﬀerential equations. .

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:

882213
Differential geometry.

LC Class. No.: QA641-670

Dewey Class. No.: 516.36

Cartan Geometries and their Symmetries = A Lie Algebroid Approach /
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