A first course in geometric topology and differential geometry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
1997
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 421 S. graph. Darst. |
| ISBN: | 0817638407 3764338407 |
Staff View
MARC
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| 245 | 1 | 0 | |a A first course in geometric topology and differential geometry |c Ethan D. Bloch |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 1997 | |
| 300 | |a XII, 421 S. |b graph. Darst. | ||
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Record in the Search Index
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Contents
Introduction ix
To the Student xi
Chapter I. Topology of Subsets of Euclidean Space 1
1.1 Introduction 1
1.2 Open and Closed Subsets of Sets in E" 2
1.3 Continuous Maps 13
1.4 Homeomorphisms and Quotient Maps 21
1.5 Connectedness 27
1.6 Compactness 34
Chapter II. Topological Surfaces 47
2.1 Introduction 47
2.2 Arcs, Disks and 1 spheres 49
2.3 Surfaces in R" 55
2.4 Surfaces Via Gluing 59
2.5 Properties of Surfaces 70
2.6 Connected Sum and the Classification of Compact
Connected Surfaces 73
Appendix A2.1 Proof of Theorem 2.4.3 (i) 82
Appendix A2.2 Proof of Theorem 2.6.1 91
Chapter III. Simplicial Surfaces 110
3.1 Introduction 110
3.2 Simplices 111
3.3 Simplicial Complexes 119
3.4 Simplicial Surfaces 131
3.5 The Euler Characteristic 137
3.6 Proof of the Classification of Compact Connected
Surfaces 141
3.7 Simplicial Curvature and the Simplicial Gauss Bonnet
Theorem 152
vi Contents
3.8 Simplicial Disks and the Brouwer Fixed Point
Theorem 157
Chapter IV. Curves in R3 167
4.1 Introduction 167
4.2 Smooth Functions 167
4.3 Curves in R3 173
4.4 Tangent, Normal and Binormal Vectors 180
4.5 Curvature and Torsion 184
4.6 Fundamental Theorem of Curves 192
4.7 Plane Curves 196
Chapter V. Smooth Surfaces 202
5.1 Introduction 202
5.2 Smooth Surfaces 202
5.3 Examples of Smooth Surfaces 214
5.4 Tangent and Normal Vectors 223
5.5 First Fundamental Form 228
5.6 Directional Derivatives Coordinate Free 235
5.7 Directional Derivatives Coordinates 242
5.8 Length and Area 252
5.9 Isometries 257
Appendix A5.1 Proof of Proposition 5.3.1 229
Chapter VI. Curvature of Smooth Surfaces 270
6.1 Introduction and First Attempt 270
6.2 The Weingarten Map and the Second Fundamental
Form 274
6.3 Curvature Second Attempt 281
6.4 Computations of Curvature Using Coordinates 291
6.5 Theorema Egregium and the Fundamental Theorem
of Surfaces 296
Chapter VII. Geodesies 309
7.1 Introduction "Straight Lines" on Surfaces 309
7.2 Geodesies 310
7.3 Shortest Paths 322
Contents vi
Chapter VIII. The Gauss Bonnet Theorem 328
8.1 Introduction 328
8.2 The Exponential Map 329
8.3 Geodesic Polar Coordinates 335
8.4 Proof of the Gauss Bonnet Theorem 345
8.5 Non Euclidean Geometry 353
Appendix A8.1 Geodesic Convexity 362
Appendix A8.2 Geodesic Triangulations 371
Appendix 381
Further Study 386
References 391
Hints for Selected Exercises 396
Index of Notation 413
Index 419 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
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| dewey-search | 516.3/63 20 516.3/63 |
| dewey-sort | 3516.3 263 220 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| indexdate | 2025-02-10T13:13:08Z |
| institution | BVB |
| isbn | 0817638407 3764338407 |
| language | English |
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| physical | XII, 421 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
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| spelling | Bloch, Ethan D. 1956- Verfasser (DE-588)143980874 aut A first course in geometric topology and differential geometry Ethan D. Bloch Boston [u.a.] Birkhäuser 1997 XII, 421 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Topology Geometry, Differential Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Geometrische Topologie (DE-588)4156724-9 gnd rswk-swf Geometrische Topologie (DE-588)4156724-9 s DE-604 Differentialgeometrie (DE-588)4012248-7 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007483370&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bloch, Ethan D. 1956- A first course in geometric topology and differential geometry Topology Geometry, Differential Differentialgeometrie (DE-588)4012248-7 gnd Geometrische Topologie (DE-588)4156724-9 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4156724-9 |
| title | A first course in geometric topology and differential geometry |
| title_auth | A first course in geometric topology and differential geometry |
| title_exact_search | A first course in geometric topology and differential geometry |
| title_full | A first course in geometric topology and differential geometry Ethan D. Bloch |
| title_fullStr | A first course in geometric topology and differential geometry Ethan D. Bloch |
| title_full_unstemmed | A first course in geometric topology and differential geometry Ethan D. Bloch |
| title_short | A first course in geometric topology and differential geometry |
| title_sort | a first course in geometric topology and differential geometry |
| topic | Topology Geometry, Differential Differentialgeometrie (DE-588)4012248-7 gnd Geometrische Topologie (DE-588)4156724-9 gnd |
| topic_facet | Topology Geometry, Differential Differentialgeometrie Geometrische Topologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007483370&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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