عنوان

Conformal Geometry of Surfaces in S4 and Quaternions.

شابک

3540453016

شابک

9783540453017

شماره

b566095

عنوان اصلي

Conformal Geometry of Surfaces in S4 and Quaternions.

نام عام مواد

[Book]

نام نخستين پديدآور

Francis E Burstall

محل نشرو پخش و غیره

Berlin, Heidelberg

نام ناشر، پخش کننده و غيره

Springer Berlin / Heidelberg

تاریخ نشرو بخش و غیره

2004

نام خاص و کميت اثر

(98 pages).

عنوان فروست

Lecture Notes in Mathematics Ser.

متن يادداشت

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.

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

Francis E Burstall

مستند نام اشخاص تاييد نشده

Dirk Ferus

مستند نام اشخاص تاييد نشده

Francis E Burstall

مستند نام اشخاص تاييد نشده

Franz Pedit

مستند نام اشخاص تاييد نشده

Katrin Leschke

مستند نام اشخاص تاييد نشده

Ulrich Pinkall

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y