Introduction to differentiable manifolds:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Springer
2002
|
| Edition: | 2. ed. |
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 243 - 245 |
| Physical Description: | XI, 250 S. graph. Darst. : 24 cm |
| ISBN: | 0387954775 |
Staff View
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| 245 | 1 | 0 | |a Introduction to differentiable manifolds |c Serge Lang |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York u.a. |b Springer |c 2002 | |
| 300 | |a XI, 250 S. |b graph. Darst. : 24 cm | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Foreword v
Acknowledgments vii
CHAPTER I
Differential Calculus 1
§1. Categories 2
§2. Finite Dimensional Vector Spaces 4
§3. Derivatives and Composition of Maps 6
§4. Integration and Taylor s Formula 9
§5. The Inverse Mapping Theorem 12
CHAPTER II
Manifolds 20
§1. Atlases, Charts, Morphisms 20
§2. Submanifolds, Immersions, Submersions 23
§3. Partitions of Unity 31
§4. Manifolds with Boundary 34
CHAPTER III
Vector Bundles 37
§1. Definition, Pull Backs 37
§2. The Tangent Bundle 45
§3. Exact Sequences of Bundles 46
§4. Operations on Vector Bundles 52
§5. Splitting of Vector Bundles 57
ix
X CONTENTS
CHAPTER IV
Vector Fields and Differential Equations 60
§1. Existence Theorem for Differential Equations 61
§2. Vector Fields, Curves, and Flows 77
§3. Sprays 85
§4. The Flow of a Spray and the Exponential Map 94
§5. Existence of Tubular Neighborhoods 98
§6. Uniqueness of Tubular Neighborhoods 101
CHAPTER V
Operations on Vector Fields and Differential Forms 105
§1. Vector Fields, Differential Operators, Brackets 105
§2. Lie Derivative Ill
§3. Exterior Derivative 113
§4. The Poincare Lemma 126
§5. Contractions and Lie Derivative 127
§6. Vector Fields and 1 Forms Under Self Duality 132
§7. The Canonical 2 Form 137
§8. Darboux s Theorem 139
CHAPTER VI
The Theorem of Frobenius 143
§1. Statement of the Theorem 143
; §2. Differential Equations Depending on a Parameter 148
§3. Proof of the Theorem 149
§4. The Global Formulation 150
§5. Lie Groups and Subgroups 153
CHAPTER VII
Metrics 158
§1. Definition and Functoriality 158
§2. The Metric Group 162
§3. Reduction to the Metric Group 165
§4. Metric Tubular Neighborhoods 168
§5. The Morse Lemma 170
§6. The Riemannian Distance 173
§7. The Canonical Spray 176
CHAPTER VIII
Integration of Differential Forms 180
§1. Sets of Measure 0 180
§2. Change of Variables Formula 184
§3. Orientation 193
§4. The Measure Associated with a Differential Form 195
CONTENTS Xi
CHAPTER IX
Stokes Theorem 200
§1. Stokes Theorem for a Rectangular Simplex 200
§2. Stokes Theorem on a Manifold 203
§3. Stokes Theorem with Singularities 207
CHAPTER X
Applications of Stokes Theorem 214
§1. The Maximal de Rham Cohomology 214
§2. Volume forms and the Divergence 221
§3. The Divergence Theorem 230
§4. Cauchy s Theorem 234
§5. The Residue Theorem 237
Bibliography 243
Index 247
|
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| dewey-raw | 516.3/6 |
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| dewey-sort | 3516.3 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV015820594 |
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| indexdate | 2024-07-09T19:09:45Z |
| institution | BVB |
| isbn | 0387954775 |
| language | English |
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| physical | XI, 250 S. graph. Darst. : 24 cm |
| publishDate | 2002 |
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| spelling | Lang, Serge 1927-2005 Verfasser (DE-588)119305119 aut Introduction to differentiable manifolds Serge Lang 2. ed. New York u.a. Springer 2002 XI, 250 S. graph. Darst. : 24 cm txt rdacontent n rdamedia nc rdacarrier Universitext Literaturverz. S. 243 - 245 Differentiable manifolds Differential topology Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd rswk-swf Differentialtopologie (DE-588)4012255-4 gnd rswk-swf Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 s DE-604 Differentialtopologie (DE-588)4012255-4 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010129535&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lang, Serge 1927-2005 Introduction to differentiable manifolds Differentiable manifolds Differential topology Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd Differentialtopologie (DE-588)4012255-4 gnd |
| subject_GND | (DE-588)4012269-4 (DE-588)4012255-4 |
| title | Introduction to differentiable manifolds |
| title_auth | Introduction to differentiable manifolds |
| title_exact_search | Introduction to differentiable manifolds |
| title_full | Introduction to differentiable manifolds Serge Lang |
| title_fullStr | Introduction to differentiable manifolds Serge Lang |
| title_full_unstemmed | Introduction to differentiable manifolds Serge Lang |
| title_short | Introduction to differentiable manifolds |
| title_sort | introduction to differentiable manifolds |
| topic | Differentiable manifolds Differential topology Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd Differentialtopologie (DE-588)4012255-4 gnd |
| topic_facet | Differentiable manifolds Differential topology Differenzierbare Mannigfaltigkeit Differentialtopologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010129535&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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