Conformal Differential Geometry

1. Front Matter

   Pages i-x

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2. Q-curvature

   Pages 1-78

3. Conformal holonomy

   Pages 79-138

4. Back Matter

   Pages 139-152

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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.

• Spinor
• Tensor
• conformal invariants
• curvature
• differential geometry
• holonomy

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)

• Institut für Mathematik, Humboldt-Universität, Berlin, Germany

  Helga Baum, Andreas Juhl

• Matematiska Institutionen, Universitet Uppsala, Uppsala, Sweden

  Andreas Juhl

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