Cartan Geometries and their Symmetries: A Lie Algebroid by Mike Crampin,David Saunders

By Mike Crampin,David Saunders

In this publication we first overview the information of Lie groupoid and Lie algebroid, and the linked suggestions of connection. We subsequent give some thought to 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 procedure, utilizing Lie algebroids instead of Lie groupoids, and particularly utilizing Lie algebroids of vector fields alongside the projection of the fibre package, might be of benefit.
We then introduce Cartan geometries, including a few instruments we will use to check them. We take, as specific examples, the 4 classical forms of geometry: affine, projective, Riemannian and conformal geometry. We additionally see how our process can begin to healthy right into a extra basic concept. ultimately, we specialize to the geometries (affine and projective) linked to direction areas and geodesics, and think about their symmetries and different properties.

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