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Cartan Geometries and their Symmetries A Lie Algebroid Approach /

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,...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Crampin, Mike (Autor), Saunders, David (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Paris : Atlantis Press : Imprint: Atlantis Press, 2016.
Edición:1st ed. 2016.
Colección:Atlantis Studies in Variational Geometry, 4
Temas:
Acceso en línea:Texto Completo
Descripción
Sumario: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.
Descripción Física:XIV, 290 p. online resource.
ISBN:9789462391925
ISSN:2214-0719 ;