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Titlebook: Cartan Geometries and their Symmetries; A Lie Algebroid Appr Mike Crampin,David Saunders Book 2016 Atlantis Press and the author(s) 2016 Ca

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书目名称Cartan Geometries and their Symmetries
副标题A Lie Algebroid Appr
编辑Mike Crampin,David Saunders
视频videohttp://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Titlebook: Cartan Geometries and their Symmetries; A Lie Algebroid Appr Mike Crampin,David Saunders Book 2016 Atlantis Press and the author(s) 2016 Ca
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
doihttps://doi.org/10.2991/978-94-6239-192-5
isbn_ebook978-94-6239-192-5Series ISSN 2214-0700 Series E-ISSN 2214-0719
issn_series 2214-0700
copyrightAtlantis Press and the author(s) 2016
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Groupoids of Fibre Morphisms, such a condition will form a group, this will obviously not be the case when we consider maps with different domains and codomains: we will obtain, instead, a groupoid. This is exactly analogous to the relationship between the fundamental group of a topological space with a given basepoint, and the fundamental groupoid of the space.
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Waldemar Adam,Lazaros Hadjiarapoglouetries which are ‘incomplete’ and which cannot be obtained as infinitesimal versions of finite Cartan geometries. We conclude the chapter with an introduction to the concept of a symmetry for a Cartan geometry.
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Cartan Geometries,etries which are ‘incomplete’ and which cannot be obtained as infinitesimal versions of finite Cartan geometries. We conclude the chapter with an introduction to the concept of a symmetry for a Cartan geometry.
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The impact of reuse on software quality,g bundle will be spheres rather than projective spaces. In this chapter we shall explain how the action of a suitable group gives rise to such a sphere as a homogeneous space, and how the corresponding Cartan geometry can be constructed.
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