Conformal Differential Geometry

Helga Baum

ISBN 10: 3764399082 / ISBN 13: 9783764399085

Editore: Springer, Basel, Birkhäuser Basel, Birkhäuser Jan 2010, 2010

Riguardo questo articolo

This item is printed on demand - it takes 3-4 days longer - Neuware -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 such operators are the Yamabe-, the Paneitz-, the Dirac- and the twistor operator. The aim of the seminar was to present the basic ideas and some of the recent developments around Q-curvature and conformal holonomy. The part on Q-curvature discusses its origin, its relevance in geometry, spectral theory and physics. Here the influence of ideas which have their origin in the AdS/CFT-correspondence becomes visible. The part on conformal holonomy describes recent classification results, its relation to Einstein metrics and to conformal Killing spinors, and related special geometries. 152 pp. Englisch.

Codice articolo 9783764399085

Dati bibliografici

• Titolo: Conformal Differential Geometry
• Editore: Springer, Basel, Birkhäuser Basel, Birkhäuser Jan 2010
• Data di pubblicazione: 2010
• Lingua: Inglese
• ISBN 10: 3764399082
• ISBN 13: 9783764399085
• Rilegatura: Taschenbuch
• Condizione: Neu

Descrizione articolo

Riassunto

This book offers recent developments regarding Q-curvature and conformal holonomy. Discussion includes Q-curvature origin, its relevance in geometry, spectral theory and physics. Here emerges the influence of ideas originating in the AdS/CFT-correspondence.

Dalla quarta di copertina

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).