Conformal Differential Geometry : Q-Curvature and Conformal Holonomy
Conformal invariants (conformally invariant tensors, conformally covariant differential operators, conformal holonomy groups etc.) are of central significance in differential geometry and physics. Well-known examples of conformally covariant operators are the Yamabe, the Paneitz, the Dirac and the t...
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| Auteurs principaux: | , , |
|---|---|
| Format: | Livre numérique |
| Langue: | Anglais |
| Publié: |
Basel :
Birkhäuser Basel
[20..].
Cham : Springer Nature |
| Édition: | 1st ed. 2010. |
| Collection: | Oberwolfach Seminars
40 |
| Accès en ligne: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Note: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Conformal differential geometry, Q-curvature and conformal holonomy, Helga Baum, Andreas Juhl, Basel, Birkhäuser, 2010, 1 vol. (X-152 p.), Oberwolfach seminars, 978-3-7643-9908-5 • Conformal Differential Geometry, Texte imprimé, 9783764399320 • Conformal differential geometry, Q-curvature and conformal holonomy, Helga Baum, Andreas Juhl, Basel, Birkhäuser, 2010, 1 vol. (X-152 p.), Oberwolfach seminars, 978-3-7643-9908-5 • Conformal Differential Geometry, Texte imprimé, 9783764399320 • Conformal differential geometry, Q-curvature and conformal holonomy, Helga Baum, Andreas Juhl, Basel, Birkhäuser, 2010, 1 vol. (X-152 p.), Oberwolfach seminars, 978-3-7643-9908-5 |
| Résumé: | Conformal invariants (conformally invariant tensors, conformally covariant differential operators, conformal holonomy groups etc.) are of central significance in differential geometry and physics. Well-known examples of conformally covariant operators are the Yamabe, the Paneitz, the Dirac and the twistor operator. These operators are intimely connected with the notion of Branson s Q-curvature. The aim of these lectures is to present the basic ideas and some of the recent developments around Q -curvature and conformal holonomy. The part on Q -curvature starts with a discussion of its origins and its relevance in geometry and spectral theory. The following lectures describe the fundamental relation between Q -curvature and scattering theory on asymptotically hyperbolic manifolds. Building on this, they introduce the recent concept of Q -curvature polynomials and use these to reveal the recursive structure of Q -curvatures. The part on conformal holonomy starts with an introduction to Cartan connections and its holonomy groups. Then we define holonomy groups of conformal manifolds, discuss its relation to Einstein metrics and recent classification results in Riemannian and Lorentzian signature. In particular, we explain the connection between conformal holonomy and conformal Killing forms and spinors, and describe Fefferman metrics in CR geometry as Lorentzian manifold with conformal holonomy SU(1,m) |
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| Description: | Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| ISBN: | 9783764399092 |
| ISSN: | 2296-5041 |
| Accès: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |