Conformal Geometry of Surfaces in S4 and Quaternions

• Main Authors: Burstall, Francis E. (Author, http://id.loc.gov/vocabulary/relators/aut), Ferus, Dirk (http://id.loc.gov/vocabulary/relators/aut), Leschke, Katrin (http://id.loc.gov/vocabulary/relators/aut), Pedit, Franz (http://id.loc.gov/vocabulary/relators/aut), Pinkall, Ulrich (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002.
• Edition: 1st ed. 2002.
• Series: Lecture Notes in Mathematics, 1772
• Subjects: Differential geometry.; Differential Geometry.

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...

Table of Contents:

• Quaternions
• Linear algebra over the quaternions
• Projective spaces
• Vector bundles
• The mean curvature sphere
• Willmore Surfaces
• Metric and affine conformal geometry
• Twistor projections
• Bäcklund transforms of Willmore surfaces
• Willmore surfaces in S3
• Spherical Willmore surfaces in HP1
• Darboux transforms
• Appendix: The bundle L. Holomorphicity and the Ejiri theorem.