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OverviewIn 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. Full Product DetailsAuthor: Mike Crampin , David SaundersPublisher: Atlantis Press (Zeger Karssen) Imprint: Atlantis Press (Zeger Karssen) Edition: 1st ed. 2016 Volume: 4 Dimensions: Width: 15.50cm , Height: 1.90cm , Length: 23.50cm Weight: 5.797kg ISBN: 9789462391918ISBN 10: 9462391912 Pages: 290 Publication Date: 30 May 2016 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsLie 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.ReviewsThe authors expose an alternative approach to Cartan geometries. ... the book offers a nice exposition of the approach to Cartan geometries via Lie algebroids, one also has to say that, apart from the approach, the book remains in quite well-known territory. (Andreas Cap, Mathematical Reviews, April 2017) Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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