Differential geometry of curves & surfaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Mineola ; New York
Dover Publications Inc.
[2016]
|
| Edition: | Revised & updated second edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | xvi, 510 Seiten Illustrationen, Diagramme |
| ISBN: | 9780486806990 0486806995 |
Staff View
MARC
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| 245 | 1 | 0 | |a Differential geometry of curves & surfaces |c Manfredo P. Do Carmo. Instituto Nacional de Matemática, Pura e Aplicada (IMPA), Rio de Janeiro, Brazil |
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| 264 | 4 | |c © 2016 | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface to the Second Edition xi
Preface xiii
Some Remarks on Using this Book xv
1. Curves 1
1-1 Introduction 1
1-2 Parametrized Curves 2
1-3 Regular Curves; Arc Length 6
1-4 The Vector Product in R3 12
1-5 The Local Theory of Curves Parametrized by Arc Length 17
1-6 The Local Canonical Form 28
1- 7 Global Properties of Plane Curves 31
2. Regular Surfaces 53
2- 1 Introduction 53
2-2 Regular Surfaces; Inverse Images of Regular Values 54
2-3 Change of Parameters; Differentiable Functions on Surface 72
2-4 The Tangent Plane; The Differential of a Map 85
2-5 The First Fundamental Form; Area 94
2-6 Orientation of Surfaces 105
2-7 A Characterization of Compact Orientable Surfaces 112
2-8 A Geometric Definition of Area 116
Appendix: A Brief Review of Continuity and Differentiability 120
X
Contents
3. The Geometry of the Gauss
3-1 Introduction 136
3-2 The Definition of the Gauss Map and Its Fundamental
Properties 137
3-3 The Gauss Map in Local Coordinates 155
3-4 Vector Fields 178
3- 5 Ruled Surfaces and Minimal Surfaces 191
Appendix: Self-Adjoint Linear Maps and Quadratic Forms 217
4. The intrinsic Geometry o
4- 1 Introduction 220
4-2 Isometries; Conformal Maps 221
4-3 The Gauss Theorem and the Equations of Compatibility 235
4-4 Parallel Transport. Geodesics. 241
4-5 The Gauss-Bonnet Theorem and Its Applications 267
4-6 The Exponential Map. Geodesic Polar Coordinates 287
4- 7 Further Properties of Geodesics; Convex Neighborhoods 302
Appendix: Proofs of the Fundamental Theorems of the Local Theory of
Curves and Surfaces 315
5, Global Differential Geometry 321
5- 1 Introduction 321
5-2 The Rigidity of the Sphere 323
5-3 Complete Surfaces. Theorem of Hopf-Rinow 331
5-4 First and Second Variations of Arc Length; Bonnet’s Theorem 344
5-5 Jacobi Fields and Conjugate Points 363
5-6 Covering Spaces; The Theorems of Hadamard 377
5-7 Global Theorems for Curves; The Fary-Milnor Theorem 396
5-8 Surfaces of Zero Gaussian Curvature 414
5-9 Jacobi’s Theorems 421
5-10 Abstract Surfaces; Further Generalizations 430
5-11 Hilbert’s Theorem 451
Appendix: Point-Set Topology of Euclidean Spaces 460
Bibliography and Comments
Hints and Answers 478
Index
|
| any_adam_object | 1 |
| author | Carmo, Manfredo Perdigão do 1928-2018 |
| author_GND | (DE-588)1022011774 |
| author_facet | Carmo, Manfredo Perdigão do 1928-2018 |
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| author_sort | Carmo, Manfredo Perdigão do 1928-2018 |
| author_variant | m p d c mpd mpdc |
| building | Verbundindex |
| bvnumber | BV045115639 |
| classification_rvk | SK 370 |
| ctrlnum | (OCoLC)951133495 (DE-599)BSZ469845902 |
| discipline | Mathematik |
| edition | Revised & updated second edition |
| format | Book |
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| id | DE-604.BV045115639 |
| illustrated | Illustrated |
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| institution | BVB |
| isbn | 9780486806990 0486806995 |
| language | English |
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| physical | xvi, 510 Seiten Illustrationen, Diagramme |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | Dover Publications Inc. |
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| spelling | Carmo, Manfredo Perdigão do 1928-2018 Verfasser (DE-588)1022011774 aut Differential geometry of curves & surfaces Manfredo P. Do Carmo. Instituto Nacional de Matemática, Pura e Aplicada (IMPA), Rio de Janeiro, Brazil Revised & updated second edition Mineola ; New York Dover Publications Inc. [2016] © 2016 xvi, 510 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Oberfläche (DE-588)4042907-6 gnd rswk-swf Fläche (DE-588)4129864-0 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Flächentheorie (DE-588)4475211-8 gnd rswk-swf Kurve (DE-588)4033824-1 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Differentialgeometrie (DE-588)4012248-7 s Oberfläche (DE-588)4042907-6 s Kurve (DE-588)4033824-1 s DE-604 Fläche (DE-588)4129864-0 s 1\p DE-604 Flächentheorie (DE-588)4475211-8 s 2\p DE-604 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=030505865&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Carmo, Manfredo Perdigão do 1928-2018 Differential geometry of curves & surfaces Oberfläche (DE-588)4042907-6 gnd Fläche (DE-588)4129864-0 gnd Differentialgeometrie (DE-588)4012248-7 gnd Flächentheorie (DE-588)4475211-8 gnd Kurve (DE-588)4033824-1 gnd |
| subject_GND | (DE-588)4042907-6 (DE-588)4129864-0 (DE-588)4012248-7 (DE-588)4475211-8 (DE-588)4033824-1 (DE-588)4151278-9 |
| title | Differential geometry of curves & surfaces |
| title_auth | Differential geometry of curves & surfaces |
| title_exact_search | Differential geometry of curves & surfaces |
| title_full | Differential geometry of curves & surfaces Manfredo P. Do Carmo. Instituto Nacional de Matemática, Pura e Aplicada (IMPA), Rio de Janeiro, Brazil |
| title_fullStr | Differential geometry of curves & surfaces Manfredo P. Do Carmo. Instituto Nacional de Matemática, Pura e Aplicada (IMPA), Rio de Janeiro, Brazil |
| title_full_unstemmed | Differential geometry of curves & surfaces Manfredo P. Do Carmo. Instituto Nacional de Matemática, Pura e Aplicada (IMPA), Rio de Janeiro, Brazil |
| title_short | Differential geometry of curves & surfaces |
| title_sort | differential geometry of curves surfaces |
| topic | Oberfläche (DE-588)4042907-6 gnd Fläche (DE-588)4129864-0 gnd Differentialgeometrie (DE-588)4012248-7 gnd Flächentheorie (DE-588)4475211-8 gnd Kurve (DE-588)4033824-1 gnd |
| topic_facet | Oberfläche Fläche Differentialgeometrie Flächentheorie Kurve Einführung |
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