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Conformal Geometry of Surface in S4 and Quaternions : Lecture Notes in Mathematics - Francis E. Burstall

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Conformal Geometry of Surface in S4 and Quaternions

By: Francis E. Burstall, Dirk Ferus, Katrin Leschke

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Paperback | 1 March 2002

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104 Pages

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22.86 x 15.24 x 0.64

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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 B¤cklund and Darboux transforms are covered, and a new proof of the classification of Willmore spheres is given.

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Non-Fiction Mathematics Geometry Differential & Riemannian Geometry

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Non-Fiction Mathematics Geometry Differential & Riemannian Geometry

Quaternions	p. 1
Linear Algebra over the Quaternions	p. 5
Projective Spaces	p. 9
Vector Bundles	p. 15
The Mean Curvature Sphere	p. 23
Willmore Surfaces	p. 31
Metric and Affine Conformal Geometry	p. 39
Twistor Projections	p. 47
Backlund Transforms of Willmore Surfaces	p. 53
Willmore Surface in S[superscript 3]	p. 61
Spherical Willmore Surfaces in [actual symbol not reproducible]P[superscript 1]	p. 67
Darboux transforms	p. 73
Appendix	p. 83
References	p. 87
Index	p. 89
Table of Contents provided by Blackwell. All Rights Reserved.

Conformal Geometry of Surface in S4 and Quaternions

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Paperback

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