Conformal geometry of surfaces in S[4] and quaternions
著者
書誌事項
Conformal geometry of surfaces in S[4] and quaternions
（Lecture notes in mathematics, 1772）
Springer, c2002
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注記
On t.p. "[4]" is superscript
Includes bibliographical references (p. [87]) and index
内容説明・目次
内容説明
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 Backlund and Darboux transforms are covered, and a new proof of the classification of Willmore spheres is given.
目次
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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