Riemannian geometry:
Saved in:
| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Princeton
Princeton Univ. Pr.
1966
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| Edition: | 6. print. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 306 S. |
Staff View
MARC
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| 100 | 1 | |a Eisenhart, Luther Pfahler |d 1876-1965 |e Verfasser |0 (DE-588)174097905 |4 aut | |
| 245 | 1 | 0 | |a Riemannian geometry |c by Luther Pfahler Eisenhart |
| 250 | |a 6. print. | ||
| 264 | 1 | |a Princeton |b Princeton Univ. Pr. |c 1966 | |
| 300 | |a VII, 306 S. | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Chapteb I
section Tensor analysis P,g(,
1. Transformation of coordinates. The summation convention 1
2. Contravariant vectors. Congruences of curves 3
3. Invariants. Covariant vectors 6
4. Tensors. Symmetric and skew symmetric tensors 9
5. Addition, subtraction and multiplication of tensors. Contraction 12
6. Coujugate symmetric tensors of the second order. Associate tensors . 14
7. The Christoffel 3 index symbols and their relations 17
8. Riemann symbols and the Riemann tensor. The Ricci tensor 19
9. Quadratic differential forms 22
10. The equivalence of symmetric quadratic differential forms 23
11. Covariant differentiation with respect to a tensor gtj 26
Chaptkk II
Introduction of a metric
12. Definition of a metric. The fundamental tensor 34
13. Angle of two vectors. Orthogonality 37
14. Differential parameters. The normals to a hypersurface 41
15. .JT tuply orthogonal systems of hypersurfaces in a K 43
16. Metric properties of a space F« immersed in a F» 44
17. Geodesies 48
18. Riemannian, normal and geodesic coordinated 53
19. Geodesic form of the linear element. Finite equations of geodesies .. 57
20. Curvature of a curve 60
21. Parallelism 62
22. Parallel displacement and the Riemann tensor 65
23. Fields of parallel vectors 67
24. Associate directions. Parallelism in a sub space 72
25. Curvature of V. at a point 79
26. The Bianehi identity. The theorem of Schur 82
27. Isometric correspondence of spaces of constant curvature. Motions
in a Fn 84
28. Conformal spaces. Spaces conformal to a flat space 89
Chapter III
Orthogonal ennuples
29. Determination of tensors by means of the components of an orthogonal
ennuple and invariants 96
yi Contents
Section Pag«
30. Coefficients of rotation. Geodesic congruences 97
31. Determinants and matrices 101
32. The orthogonal ennnple of Schmidt. Associate directions of higher
orders. The Frenet formulas for a curve in a Fn 103
33. Principal directions determined by a symmetric covariant tensor of the
second order 107
34. Geometrical interpretation of the Eicci tensor. The Bicci principal
directions 113
35. Condition that a congruence of an orthogonal ennnple be normal.... 114
36. .Jf tuply orthogonal systems of hypersurfaces 117
37. jV tuply orthogonal systems of hypersurfaces in a space conformal to
a flat space 119
38. Congruences canonical with respect to a given congruence 125
39. Spaces for which the equations of geodesies admit a first integral... 128
40. Spaces with corresponding geodesies 131
41. Certain spaces with corresponding geodesies 135
Chapter IV
The geometry of sub spaces
42. The normals to a space F» immersed in a space F« 143
43. The Gauss and Codazzi equations for a hypersurface 146
44. Curvature of a curve in a hypersurface 150
45. Principal normal curvatures of a hypersurface and lines of curvature. 152
46. Properties of the second fundamental form. Conjugate directions.
Asymptotic directions 155
47. Equations of Gauss and Codazzi for a F» immersed in a V« 159
48. Normal and relative curvatures of a curve in a F« immersed in a F™ 164
49. The second fundamental form of a F« in a F*. Conjugate and asymp¬
totic directions 166
50. Lines of curvature and mean curvature 167
51. The fundamental equations of a F. in a F», in terms of invariants and
an orthogonal ennuple 1T0
52. Minimal varieties 176
53. Hypersurfaces with indeterminate lines of curvature 179
54. Totally geodesic varieties in a space 183
Chapter V
Sub spaces of a flat space
55. The class of a space F« 18T
56. A space F» of class p l 189
57. Evolutes of a F« in an S.+r 192
58. A subspace F. of a F» immersed in an S«+, 195
59. Spaces F« of class one 197
60. Applicability of hypersurfaces of a flat space 200
Contents vii
Section Page
61. Spaces of constant curvature which are hypersurfaces of a flat space 201
62. Coordinates of Weierstrass. Motion in a space of constant curvature 204
63. Equations of geodesies in a space of constant curvature in terms of
coordinates of Weierstrass 207
64. Equations of a space V* immersed in a F« of constant curvature.... 210
65. Spaces Vn conformal to an S» 214
Chapteb VI
Groups of motions
66. Properties of continuous groups 221
67. Transitive and intransitive groups. Invariant varieties 225
68. Infinitesimal transformations which preserve geodesies 227
69. Infinitesimal conformal transformations 230
70. Infinitesimal motions. The equations of Killing 233
71. Conditions of integrability of the equations of Killing. Spaces of
constant curvature 237
72. Infinitesimal translations 239
73. Geometrical properties of the paths of a motion 240
74. Spaces V, which admit a group of motions 241
75. Intransitive groups of motions 244
76. Spaces V, admitting a G, of motions. Complete groups of motions of
order n (n + l)/2 — 1 245
77. Simply transitive groups as groups of motions 247
Bibliography 252
|
| any_adam_object | 1 |
| author | Eisenhart, Luther Pfahler 1876-1965 |
| author_GND | (DE-588)174097905 |
| author_facet | Eisenhart, Luther Pfahler 1876-1965 |
| author_role | aut |
| author_sort | Eisenhart, Luther Pfahler 1876-1965 |
| author_variant | l p e lp lpe |
| building | Verbundindex |
| bvnumber | BV002624722 |
| classification_rvk | SK 370 |
| ctrlnum | (OCoLC)247416314 (DE-599)BVBBV002624722 |
| discipline | Mathematik |
| edition | 6. print. |
| format | Book |
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| id | DE-604.BV002624722 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:47:35Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001686709 |
| oclc_num | 247416314 |
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| owner_facet | DE-91G DE-BY-TUM DE-210 |
| physical | VII, 306 S. |
| publishDate | 1966 |
| publishDateSearch | 1966 |
| publishDateSort | 1966 |
| publisher | Princeton Univ. Pr. |
| record_format | marc |
| spelling | Eisenhart, Luther Pfahler 1876-1965 Verfasser (DE-588)174097905 aut Riemannian geometry by Luther Pfahler Eisenhart 6. print. Princeton Princeton Univ. Pr. 1966 VII, 306 S. txt rdacontent n rdamedia nc rdacarrier Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Riemannsche Geometrie (DE-588)4128462-8 gnd rswk-swf Riemannsche Geometrie (DE-588)4128462-8 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=001686709&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Eisenhart, Luther Pfahler 1876-1965 Riemannian geometry Differentialgeometrie (DE-588)4012248-7 gnd Riemannsche Geometrie (DE-588)4128462-8 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4128462-8 |
| title | Riemannian geometry |
| title_auth | Riemannian geometry |
| title_exact_search | Riemannian geometry |
| title_full | Riemannian geometry by Luther Pfahler Eisenhart |
| title_fullStr | Riemannian geometry by Luther Pfahler Eisenhart |
| title_full_unstemmed | Riemannian geometry by Luther Pfahler Eisenhart |
| title_short | Riemannian geometry |
| title_sort | riemannian geometry |
| topic | Differentialgeometrie (DE-588)4012248-7 gnd Riemannsche Geometrie (DE-588)4128462-8 gnd |
| topic_facet | Differentialgeometrie Riemannsche Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001686709&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT eisenhartlutherpfahler riemanniangeometry |