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

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I. Lecture Notes aim to report new developments in all areas of mathematics quickly, informally and at a high level. Monograph manuscripts should be reasonably self-contained and rounded off. Thus they may, and often will, present not only results of the author but also related work by other people. They may be based on specialized lecture courses. Furthermore, the manuscripts should provide sufficient motivation, examples and applications. This clearly distinguishes Lecture Notes from journal articles or technical reports which normally are very concise. Articles intended for a journal but too long to be accepted by most journals, usually do not have this "lecture notes" character. For similar reasons it is unusual for doctoral theses to be accepted for the Lecture Notes series. 2. Manuscripts should be submitted (preferably in duplicate) either to one of the series editors or to Springer-Verlag, Heidelberg. In general, manuscripts will be sent out to 2 external referees for evaluation. If a decision cannot yet be reached on the basis of the first 2 reports, further referees may be contacted: the author will be informed of this. A final decision to publish can be made only on the basis of the complete manuscript, however a refereeing process leading to a preliminary decision can be based on a pre-final or incomplete manuscript. The strict minimum amount of material that will be considered should include a detailed outline describing the planned contents of each chapter, a bibliography and several sample chapters. Authors should be aware that incomplete or insufficiently close to final manuscripts almost always result in longer refereeing times and nevertheless unclear referees' recommendations, making further refereeing of a tina! draft necessary. Authors should also be aware that parallel submission of their manuscript to another publisher while under consideration for LNM will in general lead to immediate rejection. 3. Manuscripts should in general be submitted in English. Final manuscripts should contain at least 100 pages of mathematical text and should include - a table of contents; - an informative introduction, with adequate motivation and perhaps some historical remarks: it should be accessible to a reader not intimately familiar with the topic treated; - a subject index: as a rule this is genuinely helpful for the reader.

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Lecture Notes in Mathematics Editors: J.-M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris

1772

3 Berlin Heidelberg New York Barcelona Hong Kong London Milan Paris Tokyo

RE. Burstall

D. Ferus

K. Leschke R Pedit

Conformal

U. Pinkall

Geometry

of Surfaces in S4 and Quaternions

4

1011. Springer I.,

Authors Francis E. Burstall

Franz Pedit

Dept. of Mathematical Sciences University of Bath

Dept.

Claverton Down

University of Massachusetts

of Mathematics

and Statistics

Bath BA2 7AY, U.K.

1542, Lederle

E-mail. fie. burs tall@maths. bath. ac. uk

Amherst, MA 01003, U.S.A. E-mail: franz@gang. umass. edu

Dirk Ferus Katrin Leschke

Technical

Ulrich Pinkall

Un