Differential geometry of curves and surfaces:
Saved in:
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Book |
| Language: | English |
| Published: |
New Jersey [und 8 weitere]
World Scientific
[2017]
|
| Edition: | Kaiteiban |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | xii, 312 Seiten Illustrationen, Diagramme |
| ISBN: | 9789814740234 9789814740241 |
Staff View
MARC
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| 100 | 1 | |a Umehara, Masaaki |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Kyokusen to kyokumen |
| 245 | 1 | 0 | |a Differential geometry of curves and surfaces |c Masaaki Umehara, Kotaro Yamada (Tokyo Institute of Technology, Japan) ; translated by Wayne Rossman (Kobe University, Japan) |
| 250 | |a Kaiteiban |b Revised edition [1st English edition] | ||
| 264 | 1 | |a New Jersey [und 8 weitere] |b World Scientific |c [2017] | |
| 300 | |a xii, 312 Seiten |b Illustrationen, Diagramme | ||
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| 337 | |b n |2 rdamedia | ||
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| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Geometry, Differential |v Textbooks | |
| 650 | 4 | |a Curves on surfaces |v Textbooks | |
| 650 | 4 | |a Curves |v Textbooks | |
| 650 | 4 | |a Surfaces |v Textbooks | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface v
I. Curves 1
1 What exactly is a “curve” ? 1
2 Curvature and the Frenet formula.......................... 10
3 Closed curves* ........................................... 28
4 Geometry of spirals*...................................... 40
5 Space curves.............................................. 50
II. Surfaces 57
6 What exactly is a “surface”?.............................. 57
7 The first fundamental form................................ 68
8 The second fundamental form............................... 77
9 Principal and asymptotic directions....................... 89
10 Geodesics and the Gauss-Bonnet theorem.................... 99
11 Proof of the Gauss-Bonnet theorem*....................... 117
III. Surfaces from the Viewpoint of Manifolds* 131
12 Differential forms....................................... 131
13 Levi-Civita connections ................................. 138
14 The Gauss-Bonnet formula for 2-manifolds................. 148
15 Poincaré-Hopf index theorem.............................. 152
16 The Laplacian and isothermal coordinates................. 165
17 The Gauss and Codazzi equations.......................... 172
18 Cycloids as brachistochrones............................. 181
xi
xii
Differential Geometry of Curves and Surfaces
19 Geodesic triangulations of compact Riemannian
2-manifolds............................................... 184
Appendix A Supplements 193
AT A review of calculus .................................... 193
A.2 The fundamental theorems for ordinary differential
equations ................................................ 198
A. 3 Euclidean spaces......................................... 200
Appendix B Advanced Topics on Curves and Surfaces 213
B. l Evolutes and the cycloid pendulum........................ 213
B.2 Convex curves and curves of constant width............... 219
B.3 Line integrals and the isoperimetric inequality.......... 224
B.4 First fundamental forms and maps......................... 231
B.5 Curvature line coordinates and asymptotic line
coordinates............................................... 236
B.6 Surfaces with K = 0...................................... 244
B.7 A relationship between surfaces with constant Gaussian
curvature and with constant mean curvature................ 251
B.8 Surfaces of revolution of negative constant Gaussian
curvature ................................................ 259
B.9 Criteria of typical singularities....................... 261
B.10 Proof of the fundamental theorem for surfaces............ 268
Answers to Exercises 279
Bibliography 301
List of Symbols 305
Index 307
|
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| author | Umehara, Masaaki Yamada, Kotaro 1961- |
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| discipline | Mathematik |
| edition | Kaiteiban |
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| id | DE-604.BV044286463 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:48:45Z |
| institution | BVB |
| isbn | 9789814740234 9789814740241 |
| language | English |
| lccn | 016059832 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029690695 |
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| physical | xii, 312 Seiten Illustrationen, Diagramme |
| publishDate | 2017 |
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| publisher | World Scientific |
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| spelling | Umehara, Masaaki Verfasser aut Kyokusen to kyokumen Differential geometry of curves and surfaces Masaaki Umehara, Kotaro Yamada (Tokyo Institute of Technology, Japan) ; translated by Wayne Rossman (Kobe University, Japan) Kaiteiban Revised edition [1st English edition] New Jersey [und 8 weitere] World Scientific [2017] xii, 312 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Geometry, Differential Textbooks Curves on surfaces Textbooks Curves Textbooks Surfaces Textbooks Fläche (DE-588)4129864-0 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Kurve (DE-588)4033824-1 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Differentialgeometrie (DE-588)4012248-7 s Kurve (DE-588)4033824-1 s DE-604 Fläche (DE-588)4129864-0 s Yamada, Kotaro 1961- Verfasser (DE-588)1139496654 aut Rossman, Wayne trl Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029690695&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Umehara, Masaaki Yamada, Kotaro 1961- Differential geometry of curves and surfaces Geometry, Differential Textbooks Curves on surfaces Textbooks Curves Textbooks Surfaces Textbooks Fläche (DE-588)4129864-0 gnd Differentialgeometrie (DE-588)4012248-7 gnd Kurve (DE-588)4033824-1 gnd |
| subject_GND | (DE-588)4129864-0 (DE-588)4012248-7 (DE-588)4033824-1 (DE-588)4123623-3 |
| title | Differential geometry of curves and surfaces |
| title_alt | Kyokusen to kyokumen |
| title_auth | Differential geometry of curves and surfaces |
| title_exact_search | Differential geometry of curves and surfaces |
| title_full | Differential geometry of curves and surfaces Masaaki Umehara, Kotaro Yamada (Tokyo Institute of Technology, Japan) ; translated by Wayne Rossman (Kobe University, Japan) |
| title_fullStr | Differential geometry of curves and surfaces Masaaki Umehara, Kotaro Yamada (Tokyo Institute of Technology, Japan) ; translated by Wayne Rossman (Kobe University, Japan) |
| title_full_unstemmed | Differential geometry of curves and surfaces Masaaki Umehara, Kotaro Yamada (Tokyo Institute of Technology, Japan) ; translated by Wayne Rossman (Kobe University, Japan) |
| title_short | Differential geometry of curves and surfaces |
| title_sort | differential geometry of curves and surfaces |
| topic | Geometry, Differential Textbooks Curves on surfaces Textbooks Curves Textbooks Surfaces Textbooks Fläche (DE-588)4129864-0 gnd Differentialgeometrie (DE-588)4012248-7 gnd Kurve (DE-588)4033824-1 gnd |
| topic_facet | Geometry, Differential Textbooks Curves on surfaces Textbooks Curves Textbooks Surfaces Textbooks Fläche Differentialgeometrie Kurve Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029690695&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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