Constrained Willmore surfaces: symmetries of a Möbius invariant integrable system
From Bäcklund to Darboux, this monograph presents a comprehensive journey through the transformation theory of constrained Willmore surfaces, a topic of great importance in modern differential geometry and, in particular, in the field of integrable systems in Riemannian geometry. The first book on...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, UK ; New York, NY
Cambridge University Press
2021
|
| Schriftenreihe: | London Mathematical Society lecture note series
465 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | From Bäcklund to Darboux, this monograph presents a comprehensive journey through the transformation theory of constrained Willmore surfaces, a topic of great importance in modern differential geometry and, in particular, in the field of integrable systems in Riemannian geometry. The first book on this topic, it discusses in detail a spectral deformation, Bäcklund transformations and Darboux transformations, and proves that all these transformations preserve the existence of a conserved quantity, defining, in particular, transformations within the class of constant mean curvature surfaces in 3-dimensional space-forms, with, furthermore, preservation of both the space-form and the mean curvature, and bridging the gap between different approaches to the subject, classical and modern. Clearly written with extensive references, chapter introductions and self-contained accounts of the core topics, it is suitable for newcomers to the theory of constrained Wilmore surfaces. Many detailed computations and new results unavailable elsewhere in the literature make it also an appealing reference for experts |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 17 May 2021) |
| Beschreibung: | 1 Online-Ressource (xiii, 246 Seiten) |
| ISBN: | 9781108885478 |
| DOI: | 10.1017/9781108885478 |
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| isbn | 9781108885478 |
| language | English |
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| spelling | Quintino, Áurea Casinhas 1974- (DE-588)1225080584 aut Constrained Willmore surfaces symmetries of a Möbius invariant integrable system Áurea Casinhas Quintino Cambridge, UK ; New York, NY Cambridge University Press 2021 1 Online-Ressource (xiii, 246 Seiten) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 465 Title from publisher's bibliographic system (viewed on 17 May 2021) From Bäcklund to Darboux, this monograph presents a comprehensive journey through the transformation theory of constrained Willmore surfaces, a topic of great importance in modern differential geometry and, in particular, in the field of integrable systems in Riemannian geometry. The first book on this topic, it discusses in detail a spectral deformation, Bäcklund transformations and Darboux transformations, and proves that all these transformations preserve the existence of a conserved quantity, defining, in particular, transformations within the class of constant mean curvature surfaces in 3-dimensional space-forms, with, furthermore, preservation of both the space-form and the mean curvature, and bridging the gap between different approaches to the subject, classical and modern. Clearly written with extensive references, chapter introductions and self-contained accounts of the core topics, it is suitable for newcomers to the theory of constrained Wilmore surfaces. Many detailed computations and new results unavailable elsewhere in the literature make it also an appealing reference for experts Transformations (Mathematics) Möbius transformations Integrables System (DE-588)4114032-1 gnd rswk-swf Willmore-Fläche (DE-588)4844614-2 gnd rswk-swf Willmore-Fläche (DE-588)4844614-2 s Integrables System (DE-588)4114032-1 s DE-604 Erscheint auch als Druck-Ausgabe 978-1-108-79442-8 https://doi.org/10.1017/9781108885478 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Quintino, Áurea Casinhas 1974- Constrained Willmore surfaces symmetries of a Möbius invariant integrable system Transformations (Mathematics) Möbius transformations Integrables System (DE-588)4114032-1 gnd Willmore-Fläche (DE-588)4844614-2 gnd |
| subject_GND | (DE-588)4114032-1 (DE-588)4844614-2 |
| title | Constrained Willmore surfaces symmetries of a Möbius invariant integrable system |
| title_auth | Constrained Willmore surfaces symmetries of a Möbius invariant integrable system |
| title_exact_search | Constrained Willmore surfaces symmetries of a Möbius invariant integrable system |
| title_exact_search_txtP | Constrained Willmore surfaces symmetries of a Möbius invariant integrable system |
| title_full | Constrained Willmore surfaces symmetries of a Möbius invariant integrable system Áurea Casinhas Quintino |
| title_fullStr | Constrained Willmore surfaces symmetries of a Möbius invariant integrable system Áurea Casinhas Quintino |
| title_full_unstemmed | Constrained Willmore surfaces symmetries of a Möbius invariant integrable system Áurea Casinhas Quintino |
| title_short | Constrained Willmore surfaces |
| title_sort | constrained willmore surfaces symmetries of a mobius invariant integrable system |
| title_sub | symmetries of a Möbius invariant integrable system |
| topic | Transformations (Mathematics) Möbius transformations Integrables System (DE-588)4114032-1 gnd Willmore-Fläche (DE-588)4844614-2 gnd |
| topic_facet | Transformations (Mathematics) Möbius transformations Integrables System Willmore-Fläche |
| url | https://doi.org/10.1017/9781108885478 |
| work_keys_str_mv | AT quintinoaureacasinhas constrainedwillmoresurfacessymmetriesofamobiusinvariantintegrablesystem |