Conformal Geometry of Surfaces in S4 and Quaternions
Author:   Francis E. Burstall ,  Dirk Ferus ,  Katrin Leschke ,  Franz Pedit
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Edition:   2002 ed.
Volume:   1772
ISBN:  

9783540430087


Pages:   96
Publication Date:   01 January 2002
Format:   Paperback
Availability:   Out of stock   Availability explained
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

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Conformal Geometry of Surfaces in S4 and Quaternions


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Overview

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.

Full Product Details

Author:   Francis E. Burstall ,  Dirk Ferus ,  Katrin Leschke ,  Franz Pedit
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   2002 ed.
Volume:   1772
Dimensions:   Width: 15.50cm , Height: 0.50cm , Length: 23.30cm
Weight:   0.181kg
ISBN:  

9783540430087


ISBN 10:   3540430083
Pages:   96
Publication Date:   01 January 2002
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock   Availability explained
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

Quaternions.- Linear algebra over the quaternions.- Projective spaces.- Vector bundles.- The mean curvature sphere.- Willmore Surfaces.- Metric and affine conformal geometry.- Twistor projections.- Backlund transforms of Willmore surfaces.- Willmore surfaces in S3.- Spherical Willmore surfaces in HP1.- Darboux transforms.- Appendix: The bundle L. Holomorphicity and the Ejiri theorem.

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