书目名称 | Cartan Geometries and their Symmetries |
副标题 | A Lie Algebroid Appr |
编辑 | Mike Crampin,David Saunders |
视频video | http://file.papertrans.cn/223/222186/222186.mp4 |
概述 | Expounds a new approach to the theory of Cartan connections as path connections on a certain class of Lie groupoids, or as infinitesimal connections on corresponding Lie algebroids.It contains a compr |
丛书名称 | Atlantis Studies in Variational Geometry |
图书封面 |  |
描述 | 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.. |
出版日期 | Book 2016 |
关键词 | Cartan Geometry; Lie Groupoid; Lie Algebroid; Infinitesimal Symmetry; Differential Geometry |
版次 | 1 |
doi | https://doi.org/10.2991/978-94-6239-192-5 |
isbn_ebook | 978-94-6239-192-5Series ISSN 2214-0700 Series E-ISSN 2214-0719 |
issn_series | 2214-0700 |
copyright | Atlantis Press and the author(s) 2016 |