The foundations of differential geometry:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | Undetermined |
| Veröffentlicht: |
Cambridge
Univ. Press
1967
|
| Ausgabe: | Repr. |
| Schriftenreihe: | Cambridge tracts in mathematics and mathematical physics
29 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 96 S. |
Internformat
MARC
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| 245 | 1 | 0 | |a The foundations of differential geometry |c by Oswald Veblen and J. H. C. Whitehead |
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| 264 | 1 | |a Cambridge |b Univ. Press |c 1967 | |
| 300 | |a IX, 96 S. | ||
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| 490 | 1 | |a Cambridge tracts in mathematics and mathematical physics |v 29 | |
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Datensatz im Suchindex
| _version_ | 1804117259773280256 |
|---|---|
| adam_text | CONTENTS
PAGE
PREFACE . v
CHAP.
I. THE ARITHMETIC SPACE OF n DIMENSIONS
1. Arithmetic points 1
2. Linear dependence 2
3. Linear sub spaces 4
4. Linear homogeneous transformations .... 5
5. Homogeneous linear equations 7
6. Translations 8
7. Flat sub spaces 8
8. Non homogeneous linear equations 10
9. Linear transformations 11
10, 11. Affine theorems 11, 12
12. The elementary distance function 15
II. GEOMETRIES, GROUPS AND COORDINATE
SYSTEMS
1. A geometry as a mathematical science .... 17
2. Transformation groups 18
3. Geometry and group theory 19
4. An affine space 20
5. Affine spaces ......... 21
6. Euclidean metric spates 21
7. Euclidean geometry 21
8. Coordinate systems 22
9. A class of coordinate geometries 24
10. Centred affine geometry 25
11. Oriented spaces 26
12. Oriented curves 28
13. Affine parameterizations 28
14. Projective and conformal geometry 29
15. Point transformations. Automorphisms .... 30
16. Changing views of geometry 31
III. ALLOWABLE COORDINATES
1. Functions of class u 34
2. The implicit function theorem 35
3. Transformations of class u 35
4. Continuous transformations 37
viii CONTENTS
CHAP. PAOE
III. ALLOWABLE COORDINATES continued
5. Pseudo groups 37
6. w cells of class u ........ 38
7. Simple manifolds of class u 38
8. Oriented simple manifolds 39
9. Allowable coordinate systems for a simple manifold . 39
10. The differential equations of affine geometry . . . 41
11. The differential equations of the straight lines . . 43
12. Integration of the differential equations of affine geometry 44
13. Three locally flat affine spaces 45
14. Geometric objects 46
15. Regular point transformations 47
16. Geometric objects and point transformations ... 48
17. Geometric objects and their geometries .... 49
IV. CELLS AND SCALARS
1. Purpose of the chapter 50
2. / cells in n space 50
3. Implicit equations of a / cell 52
4. Scalars 53
5. Sets of n k scalars 54
6. Sets of scalar^ and oriented i cells 54
7. i spaces in the large 56
8. Local properties. Infinitesimal geometry ... 57
9. Equivalence of scalars 58
V. TANGENT SPACES
1. Differentials of a function 59
2. Transformations of differentials 60
3. Differentials at a point 60
4. Tangent spaces 61
5. Oriented tangent spaces ...... 61
6. Approximate flatness near a given point .... 62
7. Differentials and /ir cells 63
8. Geometry of the tangent spaces 64
9. Other coordinates in the tangent spaces .... 65
10. Tangent and osculating Riemannian spaces ... 66
11. Second differentials 67
12. Affine connections ........ 67
13. Parallel displacement 69
14. Affine displacement 71
15. Generalizations 72
CONTENTS i*
CHAP. PAOK
VI. A SET OF AXIOMS FOR DIFFERENTIAL
GEOMETRY
1. Purpose of the chapter 75
2. The first group of axioms 76
3. The geometry of an ra cell 76
4. The union of coordinate systems 77
5. The second group of axioms 78
6. Consequences of axioms A and B 78
7. The third group of axioms 79
8. Consequences of axioms A, B and C ... 79
9. Manifolds of class u 80
10. i spacea in the large 81
11. Regular point transformations 82
12. The pseudo group of regular point transformations . 84
VII. VARIOUS GEOMETRIES
1. Generalities 86
2. The geometry of paths 87
3. Locally flat affine spaces 89
4. Other pseudo groups 90
5. Oriented manifolds 90
6. Displacements of associated spaces 91
7. The holonomic group 92
8. Locally holonomic displacements 93
9. The holonomic group of an affine displacement . . 93
10. Displacement of orientation 94
11. Covering manifolds 95
INDEX OF DEFINITIONS 97
|
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| author | Veblen, Oswald 1880-1960 Whitehead, John Henry Constantine 1904-1960 |
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| bvnumber | BV002968554 |
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| discipline | Mathematik |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:51:34Z |
| institution | BVB |
| language | Undetermined |
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| physical | IX, 96 S. |
| publishDate | 1967 |
| publishDateSearch | 1967 |
| publishDateSort | 1967 |
| publisher | Univ. Press |
| record_format | marc |
| series | Cambridge tracts in mathematics and mathematical physics |
| series2 | Cambridge tracts in mathematics and mathematical physics |
| spelling | Veblen, Oswald 1880-1960 Verfasser (DE-588)117726516 aut The foundations of differential geometry by Oswald Veblen and J. H. C. Whitehead Repr. Cambridge Univ. Press 1967 IX, 96 S. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics and mathematical physics 29 Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 s DE-604 Whitehead, John Henry Constantine 1904-1960 Verfasser (DE-588)11733443X aut Cambridge tracts in mathematics and mathematical physics 29 (DE-604)BV001887938 29 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001858538&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Veblen, Oswald 1880-1960 Whitehead, John Henry Constantine 1904-1960 The foundations of differential geometry Cambridge tracts in mathematics and mathematical physics Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4012248-7 |
| title | The foundations of differential geometry |
| title_auth | The foundations of differential geometry |
| title_exact_search | The foundations of differential geometry |
| title_full | The foundations of differential geometry by Oswald Veblen and J. H. C. Whitehead |
| title_fullStr | The foundations of differential geometry by Oswald Veblen and J. H. C. Whitehead |
| title_full_unstemmed | The foundations of differential geometry by Oswald Veblen and J. H. C. Whitehead |
| title_short | The foundations of differential geometry |
| title_sort | the foundations of differential geometry |
| topic | Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Differentialgeometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001858538&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001887938 |
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