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Conformal Geometry of Surfaces in S4 and Quaternions

  • Authors
  • Francis E. Burstall
  • Dirk Ferus
  • Katrin Leschke
  • Franz Pedit
  • Ulrich Pinkall

Part of the Lecture Notes in Mathematics book series (LNM, volume 1772)

Table of contents

  1. Front Matter
    Pages N2-VIII
  2. Francis E. Burstall, Franz Pedit, Dirk Ferus, Katrin Leschke, Ulrich Pinkall
    Pages 1-4
  3. Francis E. Burstall, Franz Pedit, Dirk Ferus, Katrin Leschke, Ulrich Pinkall
    Pages 5-8
  4. Francis E. Burstall, Franz Pedit, Dirk Ferus, Katrin Leschke, Ulrich Pinkall
    Pages 9-14
  5. Francis E. Burstall, Franz Pedit, Dirk Ferus, Katrin Leschke, Ulrich Pinkall
    Pages 15-22
  6. Francis E. Burstall, Franz Pedit, Dirk Ferus, Katrin Leschke, Ulrich Pinkall
    Pages 23-30
  7. Francis E. Burstall, Franz Pedit, Dirk Ferus, Katrin Leschke, Ulrich Pinkall
    Pages 31-38
  8. Francis E. Burstall, Franz Pedit, Dirk Ferus, Katrin Leschke, Ulrich Pinkall
    Pages 39-46
  9. Francis E. Burstall, Franz Pedit, Dirk Ferus, Katrin Leschke, Ulrich Pinkall
    Pages 47-52
  10. Francis E. Burstall, Franz Pedit, Dirk Ferus, Katrin Leschke, Ulrich Pinkall
    Pages 53-59
  11. Francis E. Burstall, Franz Pedit, Dirk Ferus, Katrin Leschke, Ulrich Pinkall
    Pages 61-66
  12. Francis E. Burstall, Franz Pedit, Dirk Ferus, Katrin Leschke, Ulrich Pinkall
    Pages 67-72
  13. Francis E. Burstall, Franz Pedit, Dirk Ferus, Katrin Leschke, Ulrich Pinkall
    Pages 73-81
  14. Francis E. Burstall, Franz Pedit, Dirk Ferus, Katrin Leschke, Ulrich Pinkall
    Pages 83-86
  15. Francis E. Burstall, Franz Pedit, Dirk Ferus, Katrin Leschke, Ulrich Pinkall
    Pages 87-87
  16. Francis E. Burstall, Franz Pedit, Dirk Ferus, Katrin Leschke, Ulrich Pinkall
    Pages 89-89
  17. Back Matter
    Pages 91-93

About this book

Introduction

The conformal geometry of surfaces recently developed by the authors leads to a unified understanding of algebraic curve theory and the geometry of surfaces on the basis of a quaternionic-valued function theory. The book offers an elementary introduction to the subject but takes the reader to rather advanced topics. Willmore surfaces in the foursphere, their Bäcklund and Darboux transforms are covered, and a new proof of the classification of Willmore spheres is given.

Keywords

Backlund tranform Conformal surface theory Mean curvature Wilmore functional curvature darboux transforms twistor projection

Bibliographic information

  • DOI https://doi.org/10.1007/b82935
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-43008-7
  • Online ISBN 978-3-540-45301-7
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site