LEADER 03182nam 22005295 450 001 9910254062603321 005 20220331184639.0 010 $a94-6239-192-0 024 7 $a10.2991/978-94-6239-192-5 035 $a(CKB)3710000000686202 035 $a(EBL)4530839 035 $a(DE-He213)978-94-6239-192-5 035 $a(MiAaPQ)EBC4530839 035 $z(PPN)258868597 035 $a(PPN)194075397 035 $a(EXLCZ)993710000000686202 100 $a20160520d2016 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aCartan geometries and their symmetries $ea Lie algebroid approach /$fby Mike Crampin, David Saunders 205 $a1st ed. 2016. 210 1$aParis :$cAtlantis Press :$cImprint: Atlantis Press,$d2016. 215 $a1 online resource (298 p.) 225 1 $aAtlantis Studies in Variational Geometry,$x2214-0700 ;$v4 300 $aDescription based upon print version of record. 311 $a94-6239-191-2 320 $aIncludes bibliographical references and index. 327 $aLie groupoids and Lie algebroids -- Connections on Lie groupoids and Lie algebroids -- Groupoids of ?bre morphisms -- Four case studies -- Symmetries -- Cartan geometries -- A comparison with alternative approaches -- In?nitesimal Cartan geometries on TM -- Projective geometry: the full version -- Conformal geometry: the full version -- Developments and geodesics -- Cartan theory of second-order di?erential equations. . 330 $aIn this book we first review the ideas of Lie groupoid and Lie algebroid, and the associated concepts of connection. We next consider Lie groupoids of fibre morphisms of a fibre bundle, and the connections on such groupoids together with their symmetries. We also see how the infinitesimal approach, using Lie algebroids rather than Lie groupoids, and in particular using Lie algebroids of vector fields along the projection of the fibre bundle, may be of benefit. We then introduce Cartan geometries, together with a number of tools we shall use to study them. We take, as particular examples, the four classical types of geometry: affine, projective, Riemannian and conformal geometry. We also see how our approach can start to fit into a more general theory. Finally, we specialize to the geometries (affine and projective) associated with path spaces and geodesics, and consider their symmetries and other properties. 410 0$aAtlantis Studies in Variational Geometry,$x2214-0700 ;$v4 606 $aDifferential geometry 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 615 0$aDifferential geometry. 615 14$aDifferential Geometry. 676 $a515.7242 700 $aCrampin$b Mike$4aut$4http://id.loc.gov/vocabulary/relators/aut$0879549 702 $aSaunders$b David$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254062603321 996 $aCartan Geometries and their Symmetries$91963836 997 $aUNINA