Conformal Geometry of Surfaces in S4 and Quaternions

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. (Author, http://id.loc.gov/vocabulary/relators/aut), Ferus, Dirk (http://id.loc.gov/vocabulary/relators/aut), Leschke, Katrin (http://id.loc.gov/vocabulary/relators/aut), Pedit, Franz (http://id.loc.gov/vocabulary/relators/aut), Pinkall, Ulrich (http://id.loc.gov/vocabulary/relators/aut)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002.
Edition:1st ed. 2002.
Series:Lecture Notes in Mathematics, 1772
Subjects:
Differential geometry.
Differential Geometry.
Online Access:Full Text via HEAL-Link
Description
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.
Physical Description:VIII, 96 p. online resource.
ISBN:9783540453017
ISSN:0075-8434 ;
DOI:10.1007/b82935

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