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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.
Table des matières
Q-curvature.- Conformal holonomy.
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 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.
Texte suppl.
From the reviews:
“This book grew out of an Oberwolfach student seminar on recent developments in conformal differential geometry which took place in 2007. It splits into two chapters, which to a large extent are independent of each other. Each of the chapters is an extended version of a series of lectures presented by one of the authors during the seminar and offers a nice and easily readable survey of an active area of research in conformal differential geometry.” (Andreas Cap, Mathematical Reviews, Issue 2011 d)
Commentaire
From the reviews:
"This book grew out of an Oberwolfach student seminar on recent developments in conformal differential geometry which took place in 2007. It splits into two chapters, which to a large extent are independent of each other. Each of the chapters is an extended version of a series of lectures presented by one of the authors during the seminar and offers a nice and easily readable survey of an active area of research in conformal differential geometry." (Andreas Cap, Mathematical Reviews, Issue 2011 d)
