Basic elements of differential geometry and topology:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht u.a.
Kluwer Acad. Publ.
1990
|
| Series: | Mathematics and its applications / Soviet series
60 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus d. Russ. übers. |
| Physical Description: | X, 490 S. |
| ISBN: | 0792310098 |
Staff View
MARC
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| 245 | 1 | 0 | |a Basic elements of differential geometry and topology |c by S. P. Novikov and A. T. Fomenko |
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Record in the Search Index
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CONTENTS
Series Editor's Preface v
Preface vii
PART I. BASIC CONCEPTS OF DIFFERENTIAL GEOMETRY
1.1 General Concepts of Geometry 1
1.2 Coordinates in Euclidean Space 15
1.3 Riemannian Metric in a Region of Euclidean Space 24
1.4 Pseudo Euclidean Space and Lobachevsky Geometry 33
1.5 Flat Curves 46
1.6 Space Curves 54
1.7 The Theory of Surfaces in Three Dimensional Space.
Introduction 61
1.8 The Theory of Surfaces.
Riemannian Metric and the Concept of Area 70
1.9 The Theory of Surfaces.
The Area of a Region on the Surface 77
1.10 The Theory of Surfaces.
The Theory of Curvature and the Second Quadratic Form 89
1.11 The Theory of Surfaces.
Gaussian Curvature 95
1.12 The Theory of Surfaces.
Invariants of a Pair of Quadratic Forms and Euler's Theorem 105
1.13 The Language of Complex Numbers in Geometry.
Conformal Transformations. Isothermal Coordinates 114
1.14 The Concept of a Manifold and the Simplest Examples 127
1.15 Geodesies 151
PART II. TENSORS. RIEMANNIAN GEOMETRY
2.1 Rank One and Rank Two Tensors 159
2.2 Tensors of General Form. Examples 168
2.3 Algebraic Operations on Tensors 177
2.4 Symmetric and Skew Symmetric Tensors 181
2.5 Differential Calculus of Skew Symmetric Tensors of type (0, k) 188
2.6 Covariant Differentiation. Euclidean and General Connections 198
2.7 Basic Properties of Covariant Differentiation 211
x CONTENTS
2.8 Covariant Differentiation and the Riemannian Metric.
Parallel Transport of Vectors along Curves. Geodesies 221
2.9 Riemannian Curvature Tensor.
Gaussian Curvature as an Intrinsic Invariant of the Surface 234
2.10 Skew Symmetric Tensors and the Theory of Integration 245
2.11 The General Stokes Formula and Examples 268
PART m. BASIC ELEMENTS OF TOPOLOGY
3.1 Examples of Differential Forms 280
3.2 The Degree of Mapping. Homotopy 287
3.3 Applications of the Degree of a Mapping 297
3.4 Vector Fields 302
3.5 Functions on Manifolds and Vector Fields 318
3.6 Singular Points of Vector Fields. The Fundamental Group 328
3.7 The Fundamental Group and Covering 337
APPENDICES
Appendix 1 The Simplest Groups of Transformations of Euclidean
and Non Euclidean Spaces 343
Appendix 2 Some Elements of Modern Concepts of the Geometry
of the Real World 356
Appendix 3 Crystallographic Croups 385
Appendix 4 Homology Groups and Methods of their Calculation 402
Appendix 5 The Theory of Geodesies, Second Variation and
Variational Calculus 422
Appendix 6 Basic Geometric Properties of the Lobachevskian Plane 444
Appendix 7 Selected Exerices on the Material of the Course 455
Additional Material 474
References 485
Index 487 |
| any_adam_object | 1 |
| author | Novikov, Sergej P. 1938-2024 Fomenko, Anatolij Timofeevič 1945- |
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| author_sort | Novikov, Sergej P. 1938-2024 |
| author_variant | s p n sp spn a t f at atf |
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| bvnumber | BV004316635 |
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| classification_tum | MAT 530f MAT 553f |
| ctrlnum | (OCoLC)243448468 (DE-599)BVBBV004316635 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV004316635 |
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| indexdate | 2024-07-20T05:55:15Z |
| institution | BVB |
| isbn | 0792310098 |
| language | English |
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| physical | X, 490 S. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Kluwer Acad. Publ. |
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| series2 | Mathematics and its applications / Soviet series |
| spelling | Novikov, Sergej P. 1938-2024 Verfasser (DE-588)118786490 aut Elementy differencial'noj geometrii i topologii Basic elements of differential geometry and topology by S. P. Novikov and A. T. Fomenko Dordrecht u.a. Kluwer Acad. Publ. 1990 X, 490 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications / Soviet series 60 Aus d. Russ. übers. Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Riemannsche Geometrie (DE-588)4128462-8 gnd rswk-swf Topologie (DE-588)4060425-1 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 s Topologie (DE-588)4060425-1 s DE-604 Riemannsche Geometrie (DE-588)4128462-8 s Fomenko, Anatolij Timofeevič 1945- Verfasser (DE-588)119092689 aut Soviet series Mathematics and its applications 60 (DE-604)BV004708148 60 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002684152&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Novikov, Sergej P. 1938-2024 Fomenko, Anatolij Timofeevič 1945- Basic elements of differential geometry and topology Differentialgeometrie (DE-588)4012248-7 gnd Riemannsche Geometrie (DE-588)4128462-8 gnd Topologie (DE-588)4060425-1 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4128462-8 (DE-588)4060425-1 |
| title | Basic elements of differential geometry and topology |
| title_alt | Elementy differencial'noj geometrii i topologii |
| title_auth | Basic elements of differential geometry and topology |
| title_exact_search | Basic elements of differential geometry and topology |
| title_full | Basic elements of differential geometry and topology by S. P. Novikov and A. T. Fomenko |
| title_fullStr | Basic elements of differential geometry and topology by S. P. Novikov and A. T. Fomenko |
| title_full_unstemmed | Basic elements of differential geometry and topology by S. P. Novikov and A. T. Fomenko |
| title_short | Basic elements of differential geometry and topology |
| title_sort | basic elements of differential geometry and topology |
| topic | Differentialgeometrie (DE-588)4012248-7 gnd Riemannsche Geometrie (DE-588)4128462-8 gnd Topologie (DE-588)4060425-1 gnd |
| topic_facet | Differentialgeometrie Riemannsche Geometrie Topologie |
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