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Conformal Geometry of Surfaces in S4 and Quaternions
Francis E. BurstallDirk FerusKatrin LeschkeFranz PeditUlrich Pinkall
出版Springer, 2004-10-19
主題Mathematics / Geometry / DifferentialMathematics / Geometry / General
ISBN35404530169783540453017
URLhttp://books.google.com.hk/books?id=Kmx6CwAAQBAJ&hl=&source=gbs_api
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註釋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.