LEADER 03145nam 22006255 450 001 9910144596103321 005 20200703065340.0 010 $a3-540-45301-6 024 7 $a10.1007/b82935 035 $a(CKB)1000000000233237 035 $a(SSID)ssj0000322256 035 $a(PQKBManifestationID)11279126 035 $a(PQKBTitleCode)TC0000322256 035 $a(PQKBWorkID)10299255 035 $a(PQKB)11599264 035 $a(DE-He213)978-3-540-45301-7 035 $a(MiAaPQ)EBC5585259 035 $a(Au-PeEL)EBL5585259 035 $a(OCoLC)1066180806 035 $a(PPN)155189271 035 $a(EXLCZ)991000000000233237 100 $a20121227d2002 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aConformal Geometry of Surfaces in S4 and Quaternions$b[electronic resource] /$fby Francis E. Burstall, Dirk Ferus, Katrin Leschke, Franz Pedit, Ulrich Pinkall 205 $a1st ed. 2002. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2002. 215 $a1 online resource (VIII, 96 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1772 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-43008-3 327 $aQuaternions -- 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. 330 $aThe conformal geometry of surfaces recently developed by the authors leads to a unified understanding of algebraic curve theory and the geometry of surfaces on the basis of a quaternionic-valued function theory. The book offers an elementary introduction to the subject but takes the reader to rather advanced topics. Willmore surfaces in the foursphere, their Bäcklund and Darboux transforms are covered, and a new proof of the classification of Willmore spheres is given. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1772 606 $aDifferential geometry 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 615 0$aDifferential geometry. 615 14$aDifferential Geometry. 676 $a516.3/6 676 $a510 s 700 $aBurstall$b Francis E$4aut$4http://id.loc.gov/vocabulary/relators/aut$059544 702 $aFerus$b Dirk$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aLeschke$b Katrin$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aPedit$b Franz$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aPinkall$b Ulrich$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910144596103321 996 $aConformal geometry of surfaces in S4 and quaternions$9262199 997 $aUNINA