Conformal geometry of surfaces in S [sup] 4 and quaternions

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. 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. F.e. Burstall ... [et Al.]. Includes Bibliographical References (p. 87) And Index. Also Available In An Electronic Version. 1. Quaternions....Pages 1-4 2. Linear Algebra over the Quaternions....Pages 5-8 3. Projective Spaces....Pages 9-14 4. Vector Bundles....Pages 15-22 5. The Mean Curvature Sphere....Pages 23-30 6. Willmore Surfaces....Pages 31-38 7. Metric and Affine Conformal Geometry....Pages 39-46 8. Twistor Projections....Pages 47-52 9. Bäcklund Transforms of Willmore Surfaces....Pages 53-59 10. Willmore Surfaces in S 3 ....Pages 61-66 11. Spherical Willmore Surfaces in ${\mathbb{H}}P^1$ ....Pages 67-72 12. Darboux transforms....Pages 73-81 13. Appendix....Pages 83-86 References....Pages 87-87 Index....Pages 89-89