Lecture Notes in Mathematics

Conformal Geometry of Surfaces in S4 and Quaternions

Authors: Burstall, F.E., Ferus, D., Leschke, K., Pedit, F., Pinkall, U.

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  • ISBN 978-3-540-45301-7
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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 B├Ącklund and Darboux transforms are covered, and a new proof of the classification of Willmore spheres is given.

Table of contents (15 chapters)

  • 1. Quaternions

    Burstall, Francis E. (et al.)

    Pages 1-4

  • 2. Linear Algebra over the Quaternions

    Burstall, Francis E. (et al.)

    Pages 5-8

  • 3. Projective Spaces

    Burstall, Francis E. (et al.)

    Pages 9-14

  • 4. Vector Bundles

    Burstall, Francis E. (et al.)

    Pages 15-22

  • 5. The Mean Curvature Sphere

    Burstall, Francis E. (et al.)

    Pages 23-30

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-3-540-45301-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-3-540-43008-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Conformal Geometry of Surfaces in S4 and Quaternions
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1772
Copyright
2002
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-45301-7
DOI
10.1007/b82935
Softcover ISBN
978-3-540-43008-7
Series ISSN
0075-8434
Edition Number
1
Number of Pages
VIII, 96
Topics