Surfaces in classical geometries: a treatment by moving frames
Gespeichert in:
| Hauptverfasser: | , , |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
[Cham]
Springer
[2016]
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | DE-634 DE-898 DE-861 DE-91 DE-19 DE-703 DE-20 DE-824 DE-739 Volltext Inhaltsverzeichnis Abstract |
| Beschreibung: | 1 Online-Ressource (XIII, 571 Seiten, 77 illus., 61 illus. in color) |
| ISBN: | 9783319270760 |
| ISSN: | 0172-5939 |
| DOI: | 10.1007/978-3-319-27076-0 |
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Datensatz im Suchindex
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|---|---|
| adam_text |
SURFACES IN CLASSICAL GEOMETRIES
/ JENSEN, GARY R.
: 2016
TABLE OF CONTENTS / INHALTSVERZEICHNIS
1. INTRODUCTION
2. LIE GROUPS
3. THEORY OF MOVING FRAMES
4. EUCLIDEAN GEOMETRY
5. SPHERICAL GEOMETRY
6. HYPERBOLIC GEOMETRY
7. COMPLEX STRUCTURE
8. MINIMAL IMMERSIONS IN EUCLIDEAN SPACE
9. ISOTHERMIC IMMERSIONS
10. THE BONNET PROBLEM
11. CMC 1 SURFACES IN H3
12. MOEBIUS GEOMETRY
13. COMPLEX STRUCTURE AND MOEBIUS GEOMETRY
14. ISOTHERMIC IMMERSIONS IN MOEBIUS SPACE
15. LIE SPHERE GEOMETRY
SOLUTIONS TO SELECT PROBLEMS
REFERENCES
INDEX
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
SURFACES IN CLASSICAL GEOMETRIES
/ JENSEN, GARY R.
: 2016
ABSTRACT / INHALTSTEXT
DESIGNED FOR INTERMEDIATE GRADUATE STUDIES, THIS TEXT WILL BROADEN
STUDENTS' CORE KNOWLEDGE OF DIFFERENTIAL GEOMETRY PROVIDING FOUNDATIONAL
MATERIAL TO RELEVANT TOPICS IN CLASSICAL DIFFERENTIAL GEOMETRY. THE
METHOD OF MOVING FRAMES, A NATURAL MEANS FOR DISCOVERING AND PROVING
IMPORTANT RESULTS, PROVIDES THE BASIS OF TREATMENT FOR TOPICS DISCUSSED.
ITS APPLICATION IN MANY AREAS HELPS TO CONNECT THE VARIOUS GEOMETRIES
AND TO UNCOVER MANY DEEP RELATIONSHIPS, SUCH AS THE LAWSON
CORRESPONDENCE. THE NEARLY 300 PROBLEMS AND EXERCISES RANGE FROM SIMPLE
APPLICATIONS TO OPEN PROBLEMS. EXERCISES ARE EMBEDDED IN THE TEXT AS
ESSENTIAL PARTS OF THE EXPOSITION. PROBLEMS ARE COLLECTED AT THE END OF
EACH CHAPTER; SOLUTIONS TO SELECT PROBLEMS ARE GIVEN AT THE END OF THE
BOOK. MATHEMATICA, MATLAB™, AND XFIG ARE USED TO ILLUSTRATE SELECTED
CONCEPTS AND RESULTS.THE CAREFUL SELECTION OF RESULTS SERVES TO SHOW THE
READER HOW TO PROVE THE MOST IMPORTANT THEOREMS IN THE SUBJECT, WHICH
MAY BECOME THE FOUNDATION OF FUTURE PROGRESS. THE BOOK PURSUES
SIGNIFICANT RESULTS BEYOND THE STANDARD TOPICS OF AN INTRODUCTORY
DIFFERENTIAL GEOMETRY COURSE. A SAMPLE OF THESE RESULTS INCLUDES THE
WILLMORE FUNCTIONAL, THE CLASSIFICATION OF CYCLIDES OF DUPIN, THE BONNET
PROBLEM, CONSTANT MEAN CURVATURE IMMERSIONS, ISOTHERMIC IMMERSIONS, AND
THE DUALITY BETWEEN MINIMAL SURFACES IN EUCLIDEAN SPACE AND CONSTANT
MEAN CURVATURE SURFACES IN HYPERBOLIC SPACE. THE BOOK CONCLUDES WITH LIE
SPHERE GEOMETRY AND ITS SPECTACULAR RESULT THAT ALL CYCLIDES OF DUPIN
ARE LIE SPHERE EQUIVALENT. THE EXPOSITION IS RESTRICTED TO CURVES AND
SURFACES IN ORDER TO EMPHASIZE THE GEOMETRIC INTERPRETATION OF
INVARIANTS AND OTHER CONSTRUCTIONS. WORKING IN LOW DIMENSIONS HELPS
STUDENTS DEVELOP A STRONG GEOMETRIC INTUITION.ASPIRING GEOMETERS WILL
ACQUIRE A WORKING KNOWLEDGE OF CURVES AND SURFACES IN CLASSICAL
GEOMETRIES. STUDENTS WILL LEARN THE INVARIANTS OF CONFORMAL GEOMETRY AND
HOW THESE RELATE TO THE INVARIANTS OF EUCLIDEAN, SPHERICAL, AND
HYPERBOLIC GEOMETRY. THEY WILL LEARN THE FUNDAMENTALS OF LIE SPHERE
GEOMETRY, WHICH REQUIRE THE NOTION OF LEGENDRE IMMERSIONS OF A CONTACT
STRUCTURE. PREREQUISITES INCLUDE A COMPLETED ONE SEMESTER STANDARD
COURSE ON MANIFOLD THEORY
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT. |
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| author | Jensen, Gary R. 1941- Musso, Emilio 1959- Nicolodi, Lorenzo |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-319-27076-0 |
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| issn | 0172-5939 |
| language | English |
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| spelling | Jensen, Gary R. 1941- Verfasser (DE-588)108787834 aut Surfaces in classical geometries a treatment by moving frames Gary R. Jensen, Emilio Musso, Lorenzo Nicolodi [Cham] Springer [2016] © 2016 1 Online-Ressource (XIII, 571 Seiten, 77 illus., 61 illus. in color) txt rdacontent c rdamedia cr rdacarrier Universitext 0172-5939 Mathematics Convex geometry Discrete geometry Differential geometry Differential Geometry Convex and Discrete Geometry Mathematik Musso, Emilio 1959- Verfasser (DE-588)1101966254 aut Nicolodi, Lorenzo Verfasser aut Erscheint auch als Druckausgabe 978-3-319-27074-6 https://doi.org/10.1007/978-3-319-27076-0 Verlag URL des Erstveröffentlichers Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028961633&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028961633&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract |
| spellingShingle | Jensen, Gary R. 1941- Musso, Emilio 1959- Nicolodi, Lorenzo Surfaces in classical geometries a treatment by moving frames Mathematics Convex geometry Discrete geometry Differential geometry Differential Geometry Convex and Discrete Geometry Mathematik |
| title | Surfaces in classical geometries a treatment by moving frames |
| title_auth | Surfaces in classical geometries a treatment by moving frames |
| title_exact_search | Surfaces in classical geometries a treatment by moving frames |
| title_full | Surfaces in classical geometries a treatment by moving frames Gary R. Jensen, Emilio Musso, Lorenzo Nicolodi |
| title_fullStr | Surfaces in classical geometries a treatment by moving frames Gary R. Jensen, Emilio Musso, Lorenzo Nicolodi |
| title_full_unstemmed | Surfaces in classical geometries a treatment by moving frames Gary R. Jensen, Emilio Musso, Lorenzo Nicolodi |
| title_short | Surfaces in classical geometries |
| title_sort | surfaces in classical geometries a treatment by moving frames |
| title_sub | a treatment by moving frames |
| topic | Mathematics Convex geometry Discrete geometry Differential geometry Differential Geometry Convex and Discrete Geometry Mathematik |
| topic_facet | Mathematics Convex geometry Discrete geometry Differential geometry Differential Geometry Convex and Discrete Geometry Mathematik |
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