Lectures on tensor calculus and differential geometry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Groningen
Noordhoff
1962
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII,202 S. |
Staff View
MARC
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| 246 | 1 | 3 | |a Tensor calculus and differential geometry |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
chapter 1. LINEAR VECTOR SPACES
1.1 Theorems on vector spaces 1
1.2 Linear operators 6
chapter 2. METRIC VECTOR SPACES
2.1 Theorems on metric spaces 14
2.2 Reciprocal bases 17
2.3 Orthonormal frames 21
chapter 3. BILINEAR AND QUADRATIC FORMS
3.1 Bilinear forms 27
3.2 Eigenvalues and eigenvectors of a symmetric linear operator 29
3.3 Quadratic forms 32
3.4 The principal angles between two finite dimensional spaces 38
chapter 4. TENSORS
4.1 Multilinear forms 42
4.2 Tensor algebra 45
4.3 Multivectors 48
chapter 5. MANIFOLDS IN A METRIC POINT SPACE
5.1 The point space 53
5.2 The metric point space 56
5.3 Manifolds 61
5.4 Scalar invariants 65
chapter 6. CURVES
6.1 Elementary notions 71
6.2 Frenet s equations 74
6.3 Involutes and evolutes 83
6.4 Developables 87
6.5 Intrinsic equations 95
chapter 7. GEODESIC DIFFERENTIATION
7.1 The geodesic derivative 99
7.2 Geodesic curves 103
7.3 The Christoffel three index symbols 105
7.4 Laws of transformation for the Christoffel symbols 107
7.5 The components of the geodesic derivative 108
7.6 Geodesic and conformal correspondences 112
7.7 Ricci s coefficients of rotation 118
XI
XII
chapter 8. HYPERSURFACES
8.1 The fields of normals 126
8.2 The second fundamental tensor 135
8.3 Spherical representation 140
8.4 The Theorema egregium 143
chapter 9. THEORY OF CURVATURE OF GENERAL MANIFOLDS
9.1 Covariant differentiation . 146
9.2 The tensor of Riemann 154
9.3 The Riemannian curvature 162
9.4 Evaluation of the components of the tensor of Riemann 168
9.5 Geodesic mapping 171
9.6 Conformal correspondence 173
chapter 10. THEORY OF INTEGRABILITY
10.1 The conditions of integrability 178
10.2 Geodesic and conformal mapping 183
10.3 Bonnet s problem 189
BIBLIOGRAPHY 197
INDEX 198
|
| any_adam_object | 1 |
| author | Gerretsen, Johan C. H. 1907-1983 |
| author_GND | (DE-588)127523863 |
| author_facet | Gerretsen, Johan C. H. 1907-1983 |
| author_role | aut |
| author_sort | Gerretsen, Johan C. H. 1907-1983 |
| author_variant | j c h g jch jchg |
| building | Verbundindex |
| bvnumber | BV002959272 |
| classification_rvk | SK 370 |
| ctrlnum | (OCoLC)264719381 (DE-599)BVBBV002959272 |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T15:51:25Z |
| institution | BVB |
| language | English |
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| physical | XII,202 S. |
| publishDate | 1962 |
| publishDateSearch | 1962 |
| publishDateSort | 1962 |
| publisher | Noordhoff |
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| spelling | Gerretsen, Johan C. H. 1907-1983 Verfasser (DE-588)127523863 aut Lectures on tensor calculus and differential geometry Johan C. H. Gerretsen Tensor calculus and differential geometry Groningen Noordhoff 1962 XII,202 S. txt rdacontent n rdamedia nc rdacarrier Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Tensorrechnung (DE-588)4192487-3 gnd rswk-swf Tensorrechnung (DE-588)4192487-3 s DE-604 Differentialgeometrie (DE-588)4012248-7 s Mannigfaltigkeit (DE-588)4037379-4 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001852673&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gerretsen, Johan C. H. 1907-1983 Lectures on tensor calculus and differential geometry Differentialgeometrie (DE-588)4012248-7 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Tensorrechnung (DE-588)4192487-3 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4037379-4 (DE-588)4192487-3 |
| title | Lectures on tensor calculus and differential geometry |
| title_alt | Tensor calculus and differential geometry |
| title_auth | Lectures on tensor calculus and differential geometry |
| title_exact_search | Lectures on tensor calculus and differential geometry |
| title_full | Lectures on tensor calculus and differential geometry Johan C. H. Gerretsen |
| title_fullStr | Lectures on tensor calculus and differential geometry Johan C. H. Gerretsen |
| title_full_unstemmed | Lectures on tensor calculus and differential geometry Johan C. H. Gerretsen |
| title_short | Lectures on tensor calculus and differential geometry |
| title_sort | lectures on tensor calculus and differential geometry |
| topic | Differentialgeometrie (DE-588)4012248-7 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Tensorrechnung (DE-588)4192487-3 gnd |
| topic_facet | Differentialgeometrie Mannigfaltigkeit Tensorrechnung |
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