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[null,"1.","Record Nr.",null,"UNINA9910254062603321"]
[null,null,"Autore",null,"Crampin Mike"]
[null,null,"Titolo",null,"Cartan Geometries and their Symmetries : A Lie Algebroid Approach / / by Mike Crampin, David Saunders"]
[null,null,"Pubbl/distr/stampa",null,"Paris : , : Atlantis Press : , : Imprint : Atlantis Press, , 2016"]
[null,null,"ISBN",null,"94-6239-192-0"]
[null,null,"Edizione",null,"[1st ed. 2016.]"]
[null,null,"Descrizione fisica",null,"1 online resource (298 p.)"]
[null,null,"Collana",null,"Atlantis Studies in Variational Geometry, , 2214-0719 ; ; 4"]
[null,null,"Disciplina",null,"515.7242"]
[null,null,"Soggetti",null,"Geometry, Differential"]
[{"$nulls":4},"Differential Geometry"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","Description based upon print version of record."]
[null,null,null,"Nota di bibliografia","Includes bibliographical references and index."]
[null,null,"Nota di contenuto",null,"Lie groupoids and Lie algebroids -- Connections on Lie groupoids and Lie algebroids -- Groupoids of ﬁbre morphisms -- Four case studies -- Symmetries -- Cartan geometries -- A comparison with alternative approaches -- Inﬁnitesimal Cartan geometries on TM -- Projective geometry: the full version -- Conformal geometry: the full version -- Developments and geodesics -- Cartan theory of second-order diﬀerential equations. ."]
[null,null,null,"Sommario/riassunto","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."]