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Conformal Differential Geometry

Q-Curvature and Conformal Holonomy

  • Textbook
  • © 2010

Overview

Authors:
  1. Helga Baum

    1. Institut für Mathematik, Humboldt-Universität, Berlin, Germany

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  2. Andreas Juhl

    1. Institut für Mathematik, Humboldt-Universität, Berlin, Germany
      Matematiska Institutionen, Universitet Uppsala, Uppsala, Sweden

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  • Reviews very recent developments
  • Compact introduction into an active field of research

Part of the book series: Oberwolfach Seminars (OWS, volume 40)

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Table of contents (2 chapters)

  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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Keywords

About this book

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.

Reviews

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)

Authors and Affiliations

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

    Helga Baum, Andreas Juhl

  • Matematiska Institutionen, Universitet Uppsala, Uppsala, Sweden

    Andreas Juhl

Bibliographic Information

  • Book Title: Conformal Differential Geometry

  • Book Subtitle: Q-Curvature and Conformal Holonomy

  • Authors: Helga Baum, Andreas Juhl

  • Series Title: Oberwolfach Seminars

  • DOI: https://doi.org/10.1007/978-3-7643-9909-2

  • Publisher: Birkhäuser Basel

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Birkhäuser Basel 2010

  • Softcover ISBN: 978-3-7643-9908-5Published: 14 January 2010

  • eBook ISBN: 978-3-7643-9909-2Published: 28 January 2011

  • Series ISSN: 1661-237X

  • Series E-ISSN: 2296-5041

  • Edition Number: 1

  • Number of Pages: X, 152

  • Topics: Differential Geometry

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