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- catalog abstract "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.".
- catalog contributor b12449704.
- catalog created "c2002.".
- catalog date "2002".
- catalog date "c2002.".
- catalog dateCopyrighted "c2002.".
- catalog description "Includes bibliographical references (p. 87) and index.".
- catalog description "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.".
- catalog description "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.".
- catalog extent "viii, 86 p. ;".
- catalog hasFormat "Also available in an electronic version.".
- catalog identifier "3540430083 (pbk.)".
- catalog isFormatOf "Also available in an electronic version.".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1772.".
- catalog isPartOf "Lecture notes in mathematics, 0075-8434 ; 1773".
- catalog issued "2002".
- catalog issued "c2002.".
- catalog language "eng".
- catalog publisher "Berlin : Springer,".
- catalog relation "Also available in an electronic version.".
- catalog subject "Conformal geometry.".
- catalog subject "Conformal mapping.".
- catalog subject "Global differential geometry.".
- catalog subject "Mathematics.".
- catalog subject "QA3 .L28 no. 1772".
- catalog subject "Quaternions.".
- catalog subject "Surfaces, Representation of.".
- catalog tableOfContents "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.".
- catalog title "Conformal geometry of surfaces in S4 and quaternions / F.E. Burstall ... [et al.].".
- catalog type "Computer network resources. local".
- catalog type "Electronic books. lcsh".
- catalog type "text".