Painlevé equations in the differential geometry of surfaces:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2000
|
| Schriftenreihe: | Lecture notes in mathematics
1753 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VI, 120 S. |
| ISBN: | 3540414142 |
Internformat
MARC
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| 100 | 1 | |a Bobenko, Aleksandr I. |d 1960- |e Verfasser |0 (DE-588)122463625 |4 aut | |
| 245 | 1 | 0 | |a Painlevé equations in the differential geometry of surfaces |c Alexander I. Bobenko ; Ulrich Eitner |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2000 | |
| 300 | |a VI, 120 S. | ||
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Datensatz im Suchindex
| _version_ | 1804128237989658624 |
|---|---|
| adam_text | Contents
1. Introduction 1
2. Basics on Painleve Equations and Quaternionic Description of
Surfaces 7
2.1 Painleve Property and Painleve Equations 7
2.2 Isomonodromic Deformations 9
2.3 Conformally Parametrized Surfaces 16
2.4 Quaternionic Description of Surfaces 19
3. Bonnet Surfaces in Euclidean Three space 21
3.1 Definition of Bonnet Surfaces and Simplest Properties 22
3.2 Local Theory away from Critical Points 26
3.3 Local Theory at Critical Points 33
3.3.1 Index of a Critical Point 34
3.3.2 Hazzidakis Equation at Critical Points 35
3.3.3 Connection to the Local Theory away from Critical Points 39
3.4 Bonnet Surfaces via Painleve Transcendents 39
3.4.1 From the Moving Frame of Bonnet B and By Surfaces to
the Lax Representation of Painleve VI Equations 40
3.4.2 Moving Frame Equation and Lax Representation for Painleve
V 44
3.5 Global Properties of Bonnet Surfaces 49
3.5.1 Existence of Critical Points 49
3.5.2 Global Classification of Bonnet Surfaces 51
3.6 Examples of Bonnet Surfaces 54
3.6.1 Bonnet Surface of type A, B, and C 54
3.6.2 Bonnet Surfaces with Critical Points 56
3.7 Schlesinger Transformations for Bonnet Surfaces 58
3.7.1 Transformations of Painleve Equations 58
3.7.2 Schlesinger Transformations for Bonnet Surfaces of Type B 59
3.7.3 Schlesinger Transformation for Bonnet Surfaces with Crit¬
ical Points 62
VI Contents
4. Bonnet Surfaces in S3 and H3 and Surfaces with Harmonic
Inverse Mean Curvature 65
4.1 Surfaces in S3 and H3 65
4.2 Definition and Simplest Properties 67
4.3 Bonnet Surfaces in S3 and H3 away from Critical Points 68
4.4 Local Theory of Bonnet Surfaces in S3 and H3 at Critical Points 71
4.5 Bonnet surfaces in S3 and H3 in Terms of Painleve Transcendents 72
4.6 Global Properties of Bonnet Surfaces in Space Forms 74
4.7 Surfaces with Harmonic Inverse Mean Curvature 75
4.8 Bonnet Pairs of HIMC Surfaces 78
4.8.1 Basic Facts about Bonnet Pairs 78
4.8.2 Bonnet Surfaces in S3 and Bonnet Pairs of HIMC Surfaces 80
4.9 HIMC Bonnet Pairs in Painleve Transcendents 83
4.9.1 HIMC Bonnet Pairs of type A and Painleve VI Equations 83
4.9.2 HIMC Bonnet Pairs of type C and Painleve V Equations . 85
4.10 Examples of HIMC Surfaces 87
5. Surfaces with Constant Curvature 89
5.1 Surfaces with Constant Negative Gaussian Curvature and Two
Straight Asymptotic Lines 89
5.1.1 Surfaces with Constant Negative Gaussian Curvature .... 89
5.1.2 Amsler Surfaces 91
5.1.3 The asymptotic cone and self similar evolution of smoke
rings 94
5.2 Smyth surfaces 98
5.3 Affine Spheres with Affine Straight Lines 101
5.3.1 Indefinite Affine Spheres 101
5.3.2 Curves in Affine Differential Geometry and Asymptotic
Lines on Affine Spheres 103
5.3.3 Affine Spheres with Affine Straight Lines and Painleve III
Equation 105
5.3.4 Examples of Affine Spheres 107
6. Appendices 109
6.1 Appendix A. Proof of Lemma 3.3.2: Non existence of Umbilic
Points with M = 0 109
6.2 Appendix B. Proof of Lemma 3.5.1: Existence of Critical Points . Ill
References 112
Index 119
|
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| author | Bobenko, Aleksandr I. 1960- Eitner, Ulrich 1959- |
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| author_sort | Bobenko, Aleksandr I. 1960- |
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| building | Verbundindex |
| bvnumber | BV013445294 |
| classification_rvk | SI 850 SK 370 |
| classification_tum | MAT 530f |
| ctrlnum | (OCoLC)634687631 (DE-599)BVBBV013445294 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV013445294 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:46:04Z |
| institution | BVB |
| isbn | 3540414142 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009177817 |
| oclc_num | 634687631 |
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| physical | VI, 120 S. |
| publishDate | 2000 |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Bobenko, Aleksandr I. 1960- Verfasser (DE-588)122463625 aut Painlevé equations in the differential geometry of surfaces Alexander I. Bobenko ; Ulrich Eitner Berlin [u.a.] Springer 2000 VI, 120 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1753 Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Flächentheorie (DE-588)4475211-8 gnd rswk-swf Fläche (DE-588)4129864-0 gnd rswk-swf Painlevé-Gleichung (DE-588)4123902-7 gnd rswk-swf Flächentheorie (DE-588)4475211-8 s Painlevé-Gleichung (DE-588)4123902-7 s DE-604 Differentialgeometrie (DE-588)4012248-7 s Fläche (DE-588)4129864-0 s Eitner, Ulrich 1959- Verfasser (DE-588)122463641 aut Lecture notes in mathematics 1753 (DE-604)BV000676446 1753 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009177817&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bobenko, Aleksandr I. 1960- Eitner, Ulrich 1959- Painlevé equations in the differential geometry of surfaces Lecture notes in mathematics Differentialgeometrie (DE-588)4012248-7 gnd Flächentheorie (DE-588)4475211-8 gnd Fläche (DE-588)4129864-0 gnd Painlevé-Gleichung (DE-588)4123902-7 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4475211-8 (DE-588)4129864-0 (DE-588)4123902-7 |
| title | Painlevé equations in the differential geometry of surfaces |
| title_auth | Painlevé equations in the differential geometry of surfaces |
| title_exact_search | Painlevé equations in the differential geometry of surfaces |
| title_full | Painlevé equations in the differential geometry of surfaces Alexander I. Bobenko ; Ulrich Eitner |
| title_fullStr | Painlevé equations in the differential geometry of surfaces Alexander I. Bobenko ; Ulrich Eitner |
| title_full_unstemmed | Painlevé equations in the differential geometry of surfaces Alexander I. Bobenko ; Ulrich Eitner |
| title_short | Painlevé equations in the differential geometry of surfaces |
| title_sort | painleve equations in the differential geometry of surfaces |
| topic | Differentialgeometrie (DE-588)4012248-7 gnd Flächentheorie (DE-588)4475211-8 gnd Fläche (DE-588)4129864-0 gnd Painlevé-Gleichung (DE-588)4123902-7 gnd |
| topic_facet | Differentialgeometrie Flächentheorie Fläche Painlevé-Gleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009177817&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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