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Cartan geometries and their symmetries [electronic resource] : a lie algebroid approach

Cartan geometries and their symmetries [electronic resource] : a lie algebroid approach

Material type
E-Book(소장)
Personal Author
Crampin, M. Saunders, David.
Title Statement
Cartan geometries and their symmetries [electronic resource] : a lie algebroid approach / Mike Crampin, David Saunders.
Publication, Distribution, etc
Paris :   Atlantis Press :   Imprint: Atlantis Press,   2016.  
Physical Medium
1 online resource (xiv, 290 p.).
Series Statement
Atlantis studies in variational geometry,2214-0700 ; 4
ISBN
9789462391925
요약
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.
General Note
Title from e-Book title page.  
Content Notes
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. .
Bibliography, Etc. Note
Includes bibliographical references and index.
이용가능한 다른형태자료
Issued also as a book.  
Subject Added Entry-Topical Term
Lie algebroids.
Short cut
URL
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020 ▼a 9789462391925
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050 4 ▼a QA641
082 0 4 ▼a 512.55 ▼2 23
084 ▼a 512.55 ▼2 DDCK
090 ▼a 512.55
100 1 ▼a Crampin, M.
245 1 0 ▼a Cartan geometries and their symmetries ▼h [electronic resource] : ▼b a lie algebroid approach / ▼c Mike Crampin, David Saunders.
260 ▼a Paris : ▼b Atlantis Press : ▼b Imprint: Atlantis Press, ▼c 2016.
300 ▼a 1 online resource (xiv, 290 p.).
490 1 ▼a Atlantis studies in variational geometry, ▼x 2214-0700 ; ▼v 4
500 ▼a Title from e-Book title page.
504 ▼a Includes bibliographical references and index.
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.
530 ▼a Issued also as a book.
538 ▼a Mode of access: World Wide Web.
650 0 ▼a Lie algebroids.
700 1 ▼a Saunders, David.
830 0 ▼a Atlantis studies in variational geometry; ▼v v. 4.
856 4 0 ▼u https://oca.korea.ac.kr/link.n2s?url=http://dx.doi.org/10.2991/978-94-6239-192-5
945 ▼a KLPA
991 ▼a E-Book(소장)

Holdings Information

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No. 1 Location Main Library/e-Book Collection/ Call Number CR 512.55 Accession No. E14024029 Availability Loan can not(reference room) Due Date Make a Reservation Service M

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