Introduction to Möbius differential geometry:
This book introduces the reader to the geometry of surfaces and submanifolds in the conformal n-sphere. Various models for Möbius geometry are presented: the classical projective model, the quaternionic approach, and an approach that uses the Clifford algebra of the space of homogeneous coordinates...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2003
|
| Series: | London Mathematical Society lecture note series
300 |
| Subjects: | |
| Online Access: | BSB01 FHN01 Volltext |
| Summary: | This book introduces the reader to the geometry of surfaces and submanifolds in the conformal n-sphere. Various models for Möbius geometry are presented: the classical projective model, the quaternionic approach, and an approach that uses the Clifford algebra of the space of homogeneous coordinates of the classical model; the use of 2-by-2 matrices in this context is elaborated. For each model in turn applications are discussed. Topics comprise conformally flat hypersurfaces, isothermic surfaces and their transformation theory, Willmore surfaces, orthogonal systems and the Ribaucour transformation, as well as analogous discrete theories for isothermic surfaces and orthogonal systems. Certain relations with curved flats, a particular type of integrable system, are revealed. Thus this book will serve both as an introduction to newcomers (with background in Riemannian geometry and elementary differential geometry) and as a reference work for researchers |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 online resource (xi, 413 pages) |
| ISBN: | 9780511546693 |
| DOI: | 10.1017/CBO9780511546693 |
Staff View
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| 505 | 8 | |a Preliminaries: the Riemannian point of view -- The projective model -- Application: conformally flat hypersurfaces -- Application: isothermic and Willmore surfaces -- A quaternionic model -- Application: smooth and discrete isothermic surfaces -- Clifford algebra model -- A Clifford algebra model: Vahlen matrices -- Applications: orthogonal systems, isothermic surfaces | |
| 520 | |a This book introduces the reader to the geometry of surfaces and submanifolds in the conformal n-sphere. Various models for Möbius geometry are presented: the classical projective model, the quaternionic approach, and an approach that uses the Clifford algebra of the space of homogeneous coordinates of the classical model; the use of 2-by-2 matrices in this context is elaborated. For each model in turn applications are discussed. Topics comprise conformally flat hypersurfaces, isothermic surfaces and their transformation theory, Willmore surfaces, orthogonal systems and the Ribaucour transformation, as well as analogous discrete theories for isothermic surfaces and orthogonal systems. Certain relations with curved flats, a particular type of integrable system, are revealed. Thus this book will serve both as an introduction to newcomers (with background in Riemannian geometry and elementary differential geometry) and as a reference work for researchers | ||
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| author | Hertrich-Jeromin, Udo 1965- |
| author_facet | Hertrich-Jeromin, Udo 1965- |
| author_role | aut |
| author_sort | Hertrich-Jeromin, Udo 1965- |
| author_variant | u h j uhj |
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| classification_rvk | SI 320 SK 350 SK 370 |
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| contents | Preliminaries: the Riemannian point of view -- The projective model -- Application: conformally flat hypersurfaces -- Application: isothermic and Willmore surfaces -- A quaternionic model -- Application: smooth and discrete isothermic surfaces -- Clifford algebra model -- A Clifford algebra model: Vahlen matrices -- Applications: orthogonal systems, isothermic surfaces |
| ctrlnum | (ZDB-20-CBO)CR9780511546693 (OCoLC)850501532 (DE-599)BVBBV043942042 |
| dewey-full | 516.3/6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/6 |
| dewey-search | 516.3/6 |
| dewey-sort | 3516.3 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511546693 |
| format | Electronic eBook |
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| id | DE-604.BV043942042 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511546693 |
| language | English |
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| oclc_num | 850501532 |
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| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (xi, 413 pages) |
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| publishDate | 2003 |
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| publisher | Cambridge University Press |
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| series2 | London Mathematical Society lecture note series |
| spelling | Hertrich-Jeromin, Udo 1965- Verfasser aut Introduction to Möbius differential geometry Udo Hertrich-Jeromin Cambridge Cambridge University Press 2003 1 online resource (xi, 413 pages) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 300 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Preliminaries: the Riemannian point of view -- The projective model -- Application: conformally flat hypersurfaces -- Application: isothermic and Willmore surfaces -- A quaternionic model -- Application: smooth and discrete isothermic surfaces -- Clifford algebra model -- A Clifford algebra model: Vahlen matrices -- Applications: orthogonal systems, isothermic surfaces This book introduces the reader to the geometry of surfaces and submanifolds in the conformal n-sphere. Various models for Möbius geometry are presented: the classical projective model, the quaternionic approach, and an approach that uses the Clifford algebra of the space of homogeneous coordinates of the classical model; the use of 2-by-2 matrices in this context is elaborated. For each model in turn applications are discussed. Topics comprise conformally flat hypersurfaces, isothermic surfaces and their transformation theory, Willmore surfaces, orthogonal systems and the Ribaucour transformation, as well as analogous discrete theories for isothermic surfaces and orthogonal systems. Certain relations with curved flats, a particular type of integrable system, are revealed. Thus this book will serve both as an introduction to newcomers (with background in Riemannian geometry and elementary differential geometry) and as a reference work for researchers Geometry, Differential Möbius-Geometrie (DE-588)4750877-2 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Möbius-Geometrie (DE-588)4750877-2 s 1\p DE-604 Differentialgeometrie (DE-588)4012248-7 s 2\p DE-604 Erscheint auch als Druckausgabe 978-0-521-53569-4 https://doi.org/10.1017/CBO9780511546693 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hertrich-Jeromin, Udo 1965- Introduction to Möbius differential geometry Preliminaries: the Riemannian point of view -- The projective model -- Application: conformally flat hypersurfaces -- Application: isothermic and Willmore surfaces -- A quaternionic model -- Application: smooth and discrete isothermic surfaces -- Clifford algebra model -- A Clifford algebra model: Vahlen matrices -- Applications: orthogonal systems, isothermic surfaces Geometry, Differential Möbius-Geometrie (DE-588)4750877-2 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4750877-2 (DE-588)4012248-7 |
| title | Introduction to Möbius differential geometry |
| title_auth | Introduction to Möbius differential geometry |
| title_exact_search | Introduction to Möbius differential geometry |
| title_full | Introduction to Möbius differential geometry Udo Hertrich-Jeromin |
| title_fullStr | Introduction to Möbius differential geometry Udo Hertrich-Jeromin |
| title_full_unstemmed | Introduction to Möbius differential geometry Udo Hertrich-Jeromin |
| title_short | Introduction to Möbius differential geometry |
| title_sort | introduction to mobius differential geometry |
| topic | Geometry, Differential Möbius-Geometrie (DE-588)4750877-2 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Geometry, Differential Möbius-Geometrie Differentialgeometrie |
| url | https://doi.org/10.1017/CBO9780511546693 |
| work_keys_str_mv | AT hertrichjerominudo introductiontomobiusdifferentialgeometry |