03145nam 22006255 450 991014459610332120200703065340.03-540-45301-610.1007/b82935(CKB)1000000000233237(SSID)ssj0000322256(PQKBManifestationID)11279126(PQKBTitleCode)TC0000322256(PQKBWorkID)10299255(PQKB)11599264(DE-He213)978-3-540-45301-7(MiAaPQ)EBC5585259(Au-PeEL)EBL5585259(OCoLC)1066180806(PPN)155189271(EXLCZ)99100000000023323720121227d2002 u| 0engurnn|008mamaatxtccrConformal Geometry of Surfaces in S4 and Quaternions[electronic resource] /by Francis E. Burstall, Dirk Ferus, Katrin Leschke, Franz Pedit, Ulrich Pinkall1st ed. 2002.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2002.1 online resource (VIII, 96 p.) Lecture Notes in Mathematics,0075-8434 ;1772Bibliographic Level Mode of Issuance: Monograph3-540-43008-3 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.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.Lecture Notes in Mathematics,0075-8434 ;1772Differential geometryDifferential Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21022Differential geometry.Differential Geometry.516.3/6510 sBurstall Francis Eauthttp://id.loc.gov/vocabulary/relators/aut59544Ferus Dirkauthttp://id.loc.gov/vocabulary/relators/autLeschke Katrinauthttp://id.loc.gov/vocabulary/relators/autPedit Franzauthttp://id.loc.gov/vocabulary/relators/autPinkall Ulrichauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910144596103321Conformal geometry of surfaces in S4 and quaternions262199UNINA