The theory and applications of harmonic integrals:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge University Press
1989
|
| Edition: | Reissued |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 284 Seiten |
| ISBN: | 0521358817 |
Staff View
MARC
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| 245 | 1 | 0 | |a The theory and applications of harmonic integrals |c by W. V. D. Hodge |
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| 264 | 1 | |a Cambridge [u.a.] |b Cambridge University Press |c 1989 | |
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Record in the Search Index
| _version_ | 1804116999062683648 |
|---|---|
| adam_text | CONTENTS
Foreword by Sir Michael Atiyah, F.R.S. page vii
Preface xj
Chapter I. RIEMANNIAN MANIFOLDS
1. Introduction 1
2. Manifolds of class u 6
3. The Riemannian metric 11
4. Orientation 13
5. Geometry of a Riemannian manifold 16
Differential geometry 17
6. Tensors and their algebra 17
7. Numerical tensors. The metrical tensors 21
8. Parallel displacement 23
9. Covariant differentiation 28
10. Riemannian geometry 31
11. Geodesic coordinates 34
Topology 36
12. Polyhedral complexes 36
13. Complexes of class v 44
14. Manifolds 50
15. Orientation 51
16. Duality 52
17. Intersections 54
18. Product manifolds 64
Chapter H. INTEGRALS AND THEIR PERIODS
19. Multiple integrals 68
20. The theorem of Stokes 74
21. Calculus of forme 78
22. Periods 79
23. The first theorem of de Rham 87
24. Proof of de Rham s first theorem 92
25. De Rham s second theorem 100
26. Products of integrals and intersections of cycles 101
Chapter III. HARMONIC INTEGRALS
27. Definition of harmonic forms 107
28. Approximation by closed p aets 113
29. Periods of harmonic integrals 117
vi CONTENTS
30. The existence theorem: preliminary considerations page 119
31. The existence theorem, continued 130
32. Digression on the solution of integral equations 134
33. The existence theorem, concluded 139
34. De Rham s second theorem 143
35. The equations satisfied by a harmonic tensor 144
Chapter IV. APPLICATIONS TO ALGEBRAIC VARIETIES
36. Algebraic varieties 148
37. Construction of the Riemannian manifold 150
38. Discussion of the metric 154
39. The afnne connection and curvature tensor 159
40. Harmonic integrals on an algebraic manifold 165
41. The fundamental forms 168
42. An analysis of forms associated with an algebraic manifold 171
43. The classification of harmonic integrals on an algebraic
manifold 178
44. Topology of algebraic manifolds 182
45. Periods of harmonic integrals 185
46. Complex parameters 188
47. Properties of the period matrices of effective integrals 192
48. Change of metric 198
49. Some enumerative results 200
50. Defective systems of integrals 201
51. Applications to problems in algebraic geometry 212
52. Some results for surfaces 218
Chapter V. APPLICATIONS TO THE THEORY
OF CONTINUOUS GROUPS
53. Continuous groups 226
54. Geometry of the transformation space 236
55. The transformation of tensors 240
56. Invariant integrals 242
57. The group manifold 249
58. The four main classes of simple groups 258
59. The unimodular group Ln 264
60. The orthogonal group Otv+1 272
61. The orthogonal group Otv 275
62. The sympleotic group Sty 279
63. Conclusion 280
Index 282
|
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| author | Hodge, William Vallance Douglas 1903-1975 |
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| dewey-search | 515/.42 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Reissued |
| format | Book |
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| id | DE-604.BV002613977 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:47:25Z |
| institution | BVB |
| isbn | 0521358817 |
| language | English |
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| owner_facet | DE-12 DE-824 DE-188 |
| physical | XIII, 284 Seiten |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Cambridge University Press |
| record_format | marc |
| spelling | Hodge, William Vallance Douglas 1903-1975 (DE-588)1074672925 aut The theory and applications of harmonic integrals by W. V. D. Hodge Reissued Cambridge [u.a.] Cambridge University Press 1989 XIII, 284 Seiten txt rdacontent n rdamedia nc rdacarrier GROUP THEORY nasat Groupes continus INTEGRALS nasat Integraalrekening gtt Intégrales RIEMANN MANIFOLD nasat Riemann, surfaces de Continuous groups Integrals Riemann surfaces Integral (DE-588)4131477-3 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Harmonisches Integral (DE-588)4159133-1 gnd rswk-swf Harmonisches Integral (DE-588)4159133-1 s DE-604 Mannigfaltigkeit (DE-588)4037379-4 s 1\p DE-604 Integral (DE-588)4131477-3 s 2\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001680776&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 | Hodge, William Vallance Douglas 1903-1975 The theory and applications of harmonic integrals GROUP THEORY nasat Groupes continus INTEGRALS nasat Integraalrekening gtt Intégrales RIEMANN MANIFOLD nasat Riemann, surfaces de Continuous groups Integrals Riemann surfaces Integral (DE-588)4131477-3 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Harmonisches Integral (DE-588)4159133-1 gnd |
| subject_GND | (DE-588)4131477-3 (DE-588)4037379-4 (DE-588)4159133-1 |
| title | The theory and applications of harmonic integrals |
| title_auth | The theory and applications of harmonic integrals |
| title_exact_search | The theory and applications of harmonic integrals |
| title_full | The theory and applications of harmonic integrals by W. V. D. Hodge |
| title_fullStr | The theory and applications of harmonic integrals by W. V. D. Hodge |
| title_full_unstemmed | The theory and applications of harmonic integrals by W. V. D. Hodge |
| title_short | The theory and applications of harmonic integrals |
| title_sort | the theory and applications of harmonic integrals |
| topic | GROUP THEORY nasat Groupes continus INTEGRALS nasat Integraalrekening gtt Intégrales RIEMANN MANIFOLD nasat Riemann, surfaces de Continuous groups Integrals Riemann surfaces Integral (DE-588)4131477-3 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Harmonisches Integral (DE-588)4159133-1 gnd |
| topic_facet | GROUP THEORY Groupes continus INTEGRALS Integraalrekening Intégrales RIEMANN MANIFOLD Riemann, surfaces de Continuous groups Integrals Riemann surfaces Integral Mannigfaltigkeit Harmonisches Integral |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001680776&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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