Read e-book online Cartan Geometries and their Symmetries: A Lie Algebroid PDF

By Mike Crampin,David Saunders

ISBN-10: 9462391912

ISBN-13: 9789462391918

In this booklet we first evaluation the information of Lie groupoid and Lie algebroid, and the linked innovations of connection. We subsequent reflect on Lie groupoids of fibre morphisms of a  fibre package deal, and the connections on such groupoids including their symmetries. We additionally see how the infinitesimal method, utilizing Lie algebroids instead of Lie groupoids, and particularly utilizing Lie algebroids of vector fields alongside the projection of the fibre package deal, will be of benefit.
We then introduce Cartan geometries, including a few instruments we will use to review them. We take, as specific examples, the 4 classical kinds of geometry: affine, projective, Riemannian and conformal geometry. We additionally see how our strategy can begin to healthy right into a extra common conception. eventually, we specialize to the geometries (affine and projective) linked to direction areas and geodesics, and look at their symmetries and different properties.

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Cartan Geometries and their Symmetries: A Lie Algebroid Approach (Atlantis Studies in Variational Geometry) by Mike Crampin,David Saunders

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