國立虎尾科技大學 |

Cartan Geometries and their Symmetries = A Lie Algebroid Approach /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Cartan Geometries and their Symmetries/ by Mike Crampin, David Saunders.
Reminder of title:	A Lie Algebroid Approach /
Author:	Crampin, Mike.
other author:	Saunders, David.
Description:	XIV, 290 p.online resource. :
Contained By:	Springer Nature eBook
Subject:	Differential geometry. -
Online resource:	https://doi.org/10.2991/978-94-6239-192-5
ISBN:	9789462391925

Cartan Geometries and their Symmetries = A Lie Algebroid Approach /
Crampin, Mike.

Cartan Geometries and their SymmetriesA Lie Algebroid Approach /[electronic resource] :by Mike Crampin, David Saunders. - 1st ed. 2016. - XIV, 290 p.online resource. - Atlantis Studies in Variational Geometry,42214-0700 ;. - Atlantis Studies in Variational Geometry,2.

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. .

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.

ISBN: 9789462391925

Standard No.: 10.2991/978-94-6239-192-5doiSubjects--Topical Terms:

882213
Differential geometry.

LC Class. No.: QA641-670

Dewey Class. No.: 516.36

Cartan Geometries and their Symmetries = A Lie Algebroid Approach /
LDR:02724nam a22003975i 4500 001 981889
003 DE-He213
005 20200630070610.0
007 cr nn 008mamaa
008 201211s2016 fr | s |||| 0|eng d
020 $a 9789462391925 $9 978-94-6239-192-5
024 7 $a 10.2991/978-94-6239-192-5 $2 doi
035 $a 978-94-6239-192-5
050 4 $a QA641-670
072 7 $a PBMP $2 bicssc
072 7 $a MAT012030 $2 bisacsh
072 7 $a PBMP $2 thema
082 0 4 $a 516.36 $2 23
100 1 $a Crampin, Mike. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1109391
245 1 0 $a Cartan Geometries and their Symmetries $h [electronic resource] : $b A Lie Algebroid Approach / $c by Mike Crampin, David Saunders.
250 $a 1st ed. 2016.
264 1 $a Paris : $b Atlantis Press : $b Imprint: Atlantis Press, $c 2016.
300 $a XIV, 290 p. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Atlantis Studies in Variational Geometry, $x 2214-0700 ; $v 4
505 0 $a 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. .
520 $a 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.
650 0 $a Differential geometry. $3 882213
650 1 4 $a Differential Geometry. $3 671118
700 1 $a Saunders, David. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1109392
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9789462391918
776 0 8 $i Printed edition: $z 9789462391932
830 0 $a Atlantis Studies in Variational Geometry, $x 2214-0700 ; $v 2 $3 1256049
856 4 0 $u https://doi.org/10.2991/978-94-6239-192-5
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)