Metric differential geometry of curves and surfaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | Undetermined |
| Published: |
Chicago
Univ. of Chicago Press
1965
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| Edition: | 4. impr. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 216 S. Abb. |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804119881090596864 |
|---|---|
| adam_text | CONTENTS
CHAPTER PAGE
I. Curves 1
1. Introduction 1
2. Definition and equations of a curve 2
3. Arc length 7
4. The local trihedron 10
5. Curvature and torsion 18
6. Frenet formulas 22
7. The local coordinate system 27
8. The osculating sphere and the osculating circle 32
9. Shape of a curve 37
II. The Moving Trihedron 41
1. Preliminary discussion 41
2. General theory 42
3. Involutes 48
4. Evolutes 50
5. Parallel curves 53
6. The transformation of Combescure 57
7. Bertrand curves 59
III. Surfaces 63
1. Definition of a surface 63
2. Curves on surfaces 66
3. The first fundamental form 74
4. Tangent plane and normal line 76
5. Envelopes of surfaces 81
6. Developable surfaces 86
7. Ruled surfaces 92
IV. Curves on Surfaces 104
1. Transformation of parameters 104
2. Minimal curves 109
3. Angles between curves on a surface 115
4. Asymptotic curves: the second fundamental form .... 122
5. The fundamental differential equations 131
6. Conjugate nets 135
7. The lines of curvature 142
8. Geodesies 146
vii
viii CONTENTS
CHAPTEB PAOE
V. Curvature 151
1. Radius of normal curvature 151
2. Principal normal curvatures 156
3. Gaussian curvature and mean curvature 161
4. Equation of Euler: indicatrix of Dupin 165
5. A local coordinate system 170
6. Geodesic curvature 173
7. Geodesic torsion 182
VI. Transformations of Surfaces 187
1. The general analytic transformation 187
2. Conformal representation 191
3. Conformal maps of the sphere upon the plane 195
4. Applicability 198
5. Equiareal maps 202
6. Spherical indicatrix 205
7. Parallel surfaces 207
Bibliography 212
Index 213
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| any_adam_object | 1 |
| author | Lane, Ernest P. |
| author_facet | Lane, Ernest P. |
| author_role | aut |
| author_sort | Lane, Ernest P. |
| author_variant | e p l ep epl |
| building | Verbundindex |
| bvnumber | BV005693929 |
| classification_rvk | SK 370 |
| ctrlnum | (OCoLC)310687849 (DE-599)BVBBV005693929 |
| discipline | Mathematik |
| edition | 4. impr. |
| format | Book |
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| genre | Metrische Differentialgeometrie gnd |
| genre_facet | Metrische Differentialgeometrie |
| id | DE-604.BV005693929 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:33:14Z |
| institution | BVB |
| language | Undetermined |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003556308 |
| oclc_num | 310687849 |
| open_access_boolean | |
| owner | DE-703 DE-355 DE-BY-UBR |
| owner_facet | DE-703 DE-355 DE-BY-UBR |
| physical | VIII, 216 S. Abb. |
| publishDate | 1965 |
| publishDateSearch | 1965 |
| publishDateSort | 1965 |
| publisher | Univ. of Chicago Press |
| record_format | marc |
| spelling | Lane, Ernest P. Verfasser aut Metric differential geometry of curves and surfaces Ernest Preston Lane* 4. impr. Chicago Univ. of Chicago Press 1965 VIII, 216 S. Abb. txt rdacontent n rdamedia nc rdacarrier Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Kurve (DE-588)4033824-1 gnd rswk-swf Oberfläche (DE-588)4042907-6 gnd rswk-swf Fläche (DE-588)4129864-0 gnd rswk-swf Metrische Differentialgeometrie gnd rswk-swf Oberfläche (DE-588)4042907-6 s Metrische Differentialgeometrie f DE-604 Kurve (DE-588)4033824-1 s Differentialgeometrie (DE-588)4012248-7 s Fläche (DE-588)4129864-0 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003556308&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lane, Ernest P. Metric differential geometry of curves and surfaces Differentialgeometrie (DE-588)4012248-7 gnd Kurve (DE-588)4033824-1 gnd Oberfläche (DE-588)4042907-6 gnd Fläche (DE-588)4129864-0 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4033824-1 (DE-588)4042907-6 (DE-588)4129864-0 |
| title | Metric differential geometry of curves and surfaces |
| title_auth | Metric differential geometry of curves and surfaces |
| title_exact_search | Metric differential geometry of curves and surfaces |
| title_full | Metric differential geometry of curves and surfaces Ernest Preston Lane* |
| title_fullStr | Metric differential geometry of curves and surfaces Ernest Preston Lane* |
| title_full_unstemmed | Metric differential geometry of curves and surfaces Ernest Preston Lane* |
| title_short | Metric differential geometry of curves and surfaces |
| title_sort | metric differential geometry of curves and surfaces |
| topic | Differentialgeometrie (DE-588)4012248-7 gnd Kurve (DE-588)4033824-1 gnd Oberfläche (DE-588)4042907-6 gnd Fläche (DE-588)4129864-0 gnd |
| topic_facet | Differentialgeometrie Kurve Oberfläche Fläche Metrische Differentialgeometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003556308&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT laneernestp metricdifferentialgeometryofcurvesandsurfaces |