eBook

Crampin / Saunders

Cartan Geometries and their Symmetries

A Lie Algebroid Approach

sofort lieferbar!

Rezensionen ansehen

Standardpreis

96,29 €

Preisangaben inkl. MwSt. Abhängig von der Lieferadresse kann die MwSt. an der Kasse variieren. Weitere Informationen

eBook. PDF

eBook

2016

290 S. XIV, 290 p..

In englischer Sprache

Atlantis Press. ISBN 9789462391925

Das Werk ist Teil der Reihe: Atlantis Studies in Variational Geometry

Produktbeschreibung

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.