Conformal Differential Geometry

Andreas Juhl

ISBN 10: 3764399082 / ISBN 13: 9783764399085

Published by Birkhäuser Basel, Springer Basel Jan 2010, 2010

About this Item

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.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 164 pp. Englisch.

Seller Inventory # 9783764399085

Bibliographic Details

• Title: Conformal Differential Geometry
• Publisher: Birkhäuser Basel, Springer Basel Jan 2010
• Publication Date: 2010
• Language: English
• ISBN 10: 3764399082
• ISBN 13: 9783764399085
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 239W x 170H x 10D millimeters 239 millimeters width by 170 millimeters height by 10 millimeters depth
• Weight: 289 grams

About this title

Synopsis

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.

From the Back Cover

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).