Conformal Geometry of Surfaces in S4 and Quaternions

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...

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Bibliographic Details
Main Authors Burstall, Francis E, Ferus, Dirk, Leschke, Katrin, Pedit, Franz, Pinkall, Ulrich
Format eBook
LanguageEnglish
Published Berlin, Heidelberg Springer Berlin / Heidelberg 2002
Springer Berlin Heidelberg
Springer
Edition1
SeriesLecture Notes in Mathematics
Subjects
Conformal mapping
Differential Geometry
Global differential geometry
Mathematics
Mathematics and Statistics
Quaternions
Online AccessGet full text
ISBN3540430083
9783540430087
9783662196175
3662196174
ISSN0075-8434
1617-9692
DOI10.1007/b82935

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Summary: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.
ISBN:3540430083
9783540430087
9783662196175
3662196174
ISSN:0075-8434
1617-9692
DOI:10.1007/b82935