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001 978-3-540-45301-7
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007 cr nn 008mamaa
008 121227s2002 gw | s |||| 0|eng d
020 _a9783540453017
_9978-3-540-45301-7
024 7 _a10.1007/b82935
_2doi
050 4 _aQA641-670
072 7 _aPBMP
_2bicssc
072 7 _aMAT012030
_2bisacsh
072 7 _aPBMP
_2thema
082 0 4 _a516.36
_223
100 1 _aBurstall, Francis E.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aConformal Geometry of Surfaces in S4 and Quaternions
_h[electronic resource] /
_cby Francis E. Burstall, Dirk Ferus, Katrin Leschke, Franz Pedit, Ulrich Pinkall.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2002.
300 _aVIII, 96 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1772
505 0 _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.
520 _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.
650 0 _aGlobal differential geometry.
650 1 4 _aDifferential Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M21022
700 1 _aFerus, Dirk.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aLeschke, Katrin.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aPedit, Franz.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aPinkall, Ulrich.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662196175
776 0 8 _iPrinted edition:
_z9783540430087
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1772
856 4 0 _uhttps://doi.org/10.1007/b82935
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c11039
_d11039