Conformal geometry of surfaces in S 4 and quaternions:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2002
|
| Schriftenreihe: | Lecture notes in mathematics
1772 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 86 S. |
| ISBN: | 3540430083 |
Internformat
MARC
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| 245 | 1 | 0 | |a Conformal geometry of surfaces in S 4 and quaternions |c F. E. Burstall ... |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2002 | |
| 300 | |a VIII, 86 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1772 | |
| 650 | 4 | |a Conformal geometry | |
| 650 | 4 | |a Conformal mapping | |
| 650 | 4 | |a Quaternions | |
| 650 | 4 | |a Surfaces, Representation of | |
| 650 | 0 | 7 | |a Konforme Differentialgeometrie |0 (DE-588)4206468-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Quaternion |0 (DE-588)4176653-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Konforme Differentialgeometrie |0 (DE-588)4206468-5 |D s |
| 689 | 0 | 1 | |a Quaternion |0 (DE-588)4176653-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Burstall, Francis E. |e Sonstige |4 oth | |
| 830 | 0 | |a Lecture notes in mathematics |v 1772 |w (DE-604)BV000676446 |9 1772 | |
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Datensatz im Suchindex
| _version_ | 1804128925944643584 |
|---|---|
| adam_text | Table of Contents
1 Quaternions 1
1.1 The Quaternions 1
1.2 The Group S3 3
2 Linear Algebra over the Quaternions 5
2.1 Linear Maps, Complex Quaternionic Vector Spaces 5
2.2 Conformal Maps 7
3 Projective Spaces 9
3.1 Projective Spaces and Affine Coordinates 9
3.2 Metrics on MPn 11
3.3 Moebius Transformations on HP1 13
3.4 Two Spheres in S4 13
4 Vector Bundles 15
4.1 Quaternionic Vector Bundles 15
4.2 Complex Quaternionic Bundles 18
4.3 Holomorphic Quaternionic Bundles 20
5 The Mean Curvature Sphere 23
5.1 S Theory 23
5.2 The Mean Curvature Sphere 24
5.3 Hopf Fields 27
5.4 The Conformal Gauss Map 29
6 Willmore Surfaces 31
6.1 The Energy Functional 31
6.2 The Willmore Functional 35
7 Metric and AfRne Conformal Geometry 39
7.1 Surfaces in Euclidean Space 39
7.2 The Mean Curvature Sphere in Affine Coordinates 42
7.3 The Willmore Condition in Affine Coordinates 44
VIII Table of Contents
8 Twistor Projections 47
8.1 Twistor Projections 47
8.2 Super Conformal Immersions 50
9 Backlund Transforms of Willmore Surfaces 53
9.1 Backlund Transforms 53
9.2 Two Step Backlund Transforms 57
10 Willmore Surfaces in S3 61
10.1 Surfaces in S3 61
10.2 Hyperbolic 2 Planes 63
10.3 Willmore Surfaces in S3 and Minimal Surfaces in Hyperbolic
4 Space 64
11 Spherical Willmore Surfaces in HP1 67
11.1 Complex Line Bundles: Degree and Holomorphicity 67
11.2 Spherical Willmore Surfaces 71
12 Darboux tranforms 73
12.1 Riccati equations 73
12.2 Constant mean curvature surfaces in R3 74
12.3 Darboux transforms of Willmore surfaces 79
13 Appendix 83
13.1 The bundle L 83
13.2 Holomorphicity and the Ejiri/Montiel theorem 84
References 87
Index 89
|
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| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV014063398 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:57:00Z |
| institution | BVB |
| isbn | 3540430083 |
| language | English |
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| physical | VIII, 86 S. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Conformal geometry of surfaces in S 4 and quaternions F. E. Burstall ... Berlin [u.a.] Springer 2002 VIII, 86 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1772 Conformal geometry Conformal mapping Quaternions Surfaces, Representation of Konforme Differentialgeometrie (DE-588)4206468-5 gnd rswk-swf Quaternion (DE-588)4176653-2 gnd rswk-swf Konforme Differentialgeometrie (DE-588)4206468-5 s Quaternion (DE-588)4176653-2 s DE-604 Burstall, Francis E. Sonstige oth Lecture notes in mathematics 1772 (DE-604)BV000676446 1772 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009632091&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Conformal geometry of surfaces in S 4 and quaternions Lecture notes in mathematics Conformal geometry Conformal mapping Quaternions Surfaces, Representation of Konforme Differentialgeometrie (DE-588)4206468-5 gnd Quaternion (DE-588)4176653-2 gnd |
| subject_GND | (DE-588)4206468-5 (DE-588)4176653-2 |
| title | Conformal geometry of surfaces in S 4 and quaternions |
| title_auth | Conformal geometry of surfaces in S 4 and quaternions |
| title_exact_search | Conformal geometry of surfaces in S 4 and quaternions |
| title_full | Conformal geometry of surfaces in S 4 and quaternions F. E. Burstall ... |
| title_fullStr | Conformal geometry of surfaces in S 4 and quaternions F. E. Burstall ... |
| title_full_unstemmed | Conformal geometry of surfaces in S 4 and quaternions F. E. Burstall ... |
| title_short | Conformal geometry of surfaces in S 4 and quaternions |
| title_sort | conformal geometry of surfaces in s 4 and quaternions |
| topic | Conformal geometry Conformal mapping Quaternions Surfaces, Representation of Konforme Differentialgeometrie (DE-588)4206468-5 gnd Quaternion (DE-588)4176653-2 gnd |
| topic_facet | Conformal geometry Conformal mapping Quaternions Surfaces, Representation of Konforme Differentialgeometrie Quaternion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009632091&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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