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  • Book
  • © 2002

Conformal Geometry of Surfaces in S4 and Quaternions

Authors:

  1. Francis E. Burstall
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  2. Dirk Ferus
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  3. Katrin Leschke
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  4. Franz Pedit
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  5. Ulrich Pinkall
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1772)

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Table of contents (15 chapters)

  1. Front Matter

    Pages N2-VIII
    PDF

  2. 1. Quaternions

    • Francis E. Burstall, Franz Pedit, Dirk Ferus, Katrin Leschke, Ulrich Pinkall
    Pages 1-4

  3. 2. Linear Algebra over the Quaternions

    • Francis E. Burstall, Franz Pedit, Dirk Ferus, Katrin Leschke, Ulrich Pinkall
    Pages 5-8

  4. 3. Projective Spaces

    • Francis E. Burstall, Franz Pedit, Dirk Ferus, Katrin Leschke, Ulrich Pinkall
    Pages 9-14

  5. 4. Vector Bundles

    • Francis E. Burstall, Franz Pedit, Dirk Ferus, Katrin Leschke, Ulrich Pinkall
    Pages 15-22

  6. 5. The Mean Curvature Sphere

    • Francis E. Burstall, Franz Pedit, Dirk Ferus, Katrin Leschke, Ulrich Pinkall
    Pages 23-30

  7. 6. Willmore Surfaces

    • Francis E. Burstall, Franz Pedit, Dirk Ferus, Katrin Leschke, Ulrich Pinkall
    Pages 31-38

  8. 7. Metric and Affine Conformal Geometry

    • Francis E. Burstall, Franz Pedit, Dirk Ferus, Katrin Leschke, Ulrich Pinkall
    Pages 39-46

  9. 8. Twistor Projections

    • Francis E. Burstall, Franz Pedit, Dirk Ferus, Katrin Leschke, Ulrich Pinkall
    Pages 47-52

  10. 9. Bäcklund Transforms of Willmore Surfaces

    • Francis E. Burstall, Franz Pedit, Dirk Ferus, Katrin Leschke, Ulrich Pinkall
    Pages 53-59

  11. 10. Willmore Surfaces in S3

    • Francis E. Burstall, Franz Pedit, Dirk Ferus, Katrin Leschke, Ulrich Pinkall
    Pages 61-66

  12. 11. Spherical Willmore Surfaces in \({\mathbb{H}}P^1\)

    • Francis E. Burstall, Franz Pedit, Dirk Ferus, Katrin Leschke, Ulrich Pinkall
    Pages 67-72

  13. 12. Darboux transforms

    • Francis E. Burstall, Franz Pedit, Dirk Ferus, Katrin Leschke, Ulrich Pinkall
    Pages 73-81

  14. 13. Appendix

    • Francis E. Burstall, Franz Pedit, Dirk Ferus, Katrin Leschke, Ulrich Pinkall
    Pages 83-86

  15. References

    • Francis E. Burstall, Franz Pedit, Dirk Ferus, Katrin Leschke, Ulrich Pinkall
    Pages 87-87

  16. Index

    • Francis E. Burstall, Franz Pedit, Dirk Ferus, Katrin Leschke, Ulrich Pinkall
    Pages 89-89

  17. Back Matter

    Pages 91-93
    PDF
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About this book

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.
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Keywords

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Bibliographic Information

  • Book Title: Conformal Geometry of Surfaces in S4 and Quaternions

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

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/b82935

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2002

  • Softcover ISBN: 978-3-540-43008-7Published: 01 January 2002

  • eBook ISBN: 978-3-540-45301-7Published: 19 October 2004

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 96

  • Topics: Differential Geometry

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Buy it now

eBook USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

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