Author	Burstall, Francis E. author
Title	Conformal Geometry of Surfaces in S4 and Quaternions [electronic resource] / by Francis E. Burstall, Dirk Ferus, Katrin Leschke, Franz Pedit, Ulrich Pinkall
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg, 2002
Connect to	http://dx.doi.org/10.1007/b82935
Descript	VIII, 96 p. online resource

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 Bรคcklund and Darboux transforms are covered, and a new proof of the classification of Willmore spheres is given

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

1. Mathematics
2. Differential geometry
3. Mathematics
4. Differential Geometry