Download e-book for kindle: Cartan Geometries and their Symmetries: A Lie Algebroid by Mike Crampin,David Saunders

By Mike Crampin,David Saunders

ISBN-10: 9462391912

ISBN-13: 9789462391918

In this e-book we first evaluation the tips of Lie groupoid and Lie algebroid, and the linked ideas 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 process, utilizing Lie algebroids instead of Lie groupoids, and specifically utilizing Lie algebroids of vector fields alongside the projection of the fibre package, will be of benefit.
We then introduce Cartan geometries, including a couple of instruments we will use to check them. We take, as specific examples, the 4 classical different types of geometry: affine, projective, Riemannian and conformal geometry. We additionally see how our method can begin to healthy right into a extra common conception. ultimately, we specialize to the geometries (affine and projective) linked to direction areas and geodesics, and view 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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