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" Conformal Geometry of Surfaces in S4 and Quaternions. "
Francis E Burstall
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BL
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| Record Number
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746146
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b566095
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| Main Entry
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Francis E Burstall
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| Title & Author
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Conformal Geometry of Surfaces in S4 and Quaternions.\ Francis E Burstall
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| Publication Statement
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Berlin, Heidelberg : Springer Berlin / Heidelberg, 2004
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| Series Statement
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Lecture Notes in Mathematics Ser.
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(98 pages).
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| ISBN
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3540453016
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: 9783540453017
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| Contents
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Intro; 1 Quaternions; 1.1 The Quaternions; 1.2 The Group; 2 Linear Algebra over the Quaternions; 2.1 Linear Maps, Complex Quaternionic Vector Spaces; 2.2 Conformal Maps; 3 Projective Spaces; 3.1 Projective Spaces and Affine Coordinates; 3.2 Metrics on HPn; 3.3 Moebius Transformations on HP1; 3.4 Two-Spheres in S4; 4 Vector Bundles; 4.1 Quaternionic Vector Bundles; 4.2 Complex Quaternionic Bundles; 4.3 Holomorphic Quaternionic Bundles; 5 The Mean Curvature Sphere; 5.1 S-Theory; 5.2 The Mean Curvature Sphere; 5.3 Hopf Fields; 5.4 The Conformal Gauss Map; 6 Willmore Surfaces. 6.1 The Energy Functional6.2 The Willmore Functional; 7 Metric and Affine Conformal Geometry; 7.1 Surfaces in Euclidean Space; 7.2 The Mean Curvature Sphere in Affine Coordinates; 7.3 The Willmore Condition in Affine Coordinates; 8 Twistor Projections; 8.1 Twistor Projections; 8.2 Super-Conformal Immersions; 9 Bäcklund Transforms of Willmore Surfaces; 9.1 Bäcklund Transforms; 9.2 Two-Step Bäcklund Transforms; 10 Willmore Surfaces in; 10.1 Surfaces in; 10.2 Hyperbolic 2-Planes; 10.3 Willmore Surfaces in and Minimal Surfaces in Hyperbolic 4-Space; 11 Spherical Willmore Surfaces in. 11.1 Complex Line Bundles: Degree and Holomorphicity11.2 Spherical Willmore Surfaces; 12 Darboux tranforms; 12.1 Riccati equations; 12.2 Constant mean curvature surfaces in; 12.3 Darboux transforms of Willmore surfaces; 13 Appendix; 13.1 The bundle; 13.2 Holomorphicity and the Ejiri/Montiel theorem; Blank Page; Blank Page; Blank Page; Blank Page.
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| LC Classification
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QA3.F736 2004
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| Added Entry
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Dirk Ferus
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Francis E Burstall
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Franz Pedit
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Katrin Leschke
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Ulrich Pinkall
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