Cartan geometries and their symmetries [electronic resource] : a lie algebroid approach / Mike Crampin, David Saunders.

Unlimited

Authorized users

Can lend chapters, not whole ebooks

Cartan geometries and their symmetries [electronic resource] : a lie algebroid approach / Mike Crampin, David Saunders.

9789462391925 (electronic book)
9462391920 (electronic book)
9789462391918 print

[Place of publication not identified] : Atlantis Press, 2016.

English

1 online resource.

QA641

512/.55

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.

Includes bibliographical references and index.

Access limited to authorized users.

Online resource; title from PDF title page (SpringerLink, viewed May 24, 2016).

Atlantis studies in variational geometry ; v. 4.

Online Resources > Ebooks
All Resources