The geometry of Lagrange spaces: theory and applications
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht u.a.
Kluwer
1994
|
| Schriftenreihe: | Fundamental theories of physics
59 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 285 S. |
| ISBN: | 0792325915 |
Internformat
MARC
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| 100 | 1 | |a Miron, Radu |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The geometry of Lagrange spaces |b theory and applications |c by Radu Miron and Mihai Anastasiei |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer |c 1994 | |
| 300 | |a XIV, 285 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Fundamental theories of physics |v 59 | |
| 650 | 7 | |a Géométrie différentielle |2 ram | |
| 650 | 7 | |a Physique mathématique |2 ram | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Geometry, Differential | |
| 650 | 4 | |a Lagrange spaces | |
| 650 | 4 | |a Mathematical physics | |
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Datensatz im Suchindex
| _version_ | 1804124311605215232 |
|---|---|
| adam_text | Contents
Preface ix
Chapter I. Fibre Bundles. General Theory 1
1. Fibre Bundles 1
2. Principal Fibre Bundles 3
3. Vector Bundles 7
4. Morphisms of Vector Bundles 11
5. Vector Subbundles 13
6. Operations with Vector Bundles 14
7. Principal Bundle Associated with a Vector Bundle 15
8. Sections in Vector Bundles 16
Chapter II. Connections in Fibre Bundles 19
1. Non linear Connections in Vector Bundles 19
2. Local Representations of a Non linear Connection 21
3. Other Characterisations of a Non linear Connection 23
4. Vertical and Horizontal Lifts 27
5. Curvature of a Non linear Connection 30
6. Affine Morphisms of Vector Bundles 33
Chapter III. Geometry of the Total Space of a Vector Bundle 35
1. d Connections on the Total Space of a Vector Bundle 35
2. Local Representation of d Connections 40
3. Torsion and Curvature of d Connections 44
4. Structure Equations of a d Connection 51
5. Metric Structures on the Total Space of a Vector Bundle 55
Chapter IV. Geometrical Theory of Embeddings of Vector Bundles 66
1. Embeddings of Vector Bundles 66
2. Moving Frame on E1 in E 68
3. Induced Non linear Connections. Relative Covariant Derivative 70
4. The Gauss Weingarten Formulae 75
5. The Gauss Codazzi Equations 78
Chapter V. Einstein Equations 80
1. Einstein Equations 80
2. Einstein Equations in the Case m = 1 84
3. Another Form of the Einstein Equations 87
4. Einstein Equations for some particular metrics on E 90
v
vi
Chapter VI. Generalized Einstein Yang Mills Equations 94
1. Gauge Transformations 94
2. Gauge Covariant Derivatives 98
3. Metrical Gauge d Connections 101
4. Generalized Einstein Yang Mills Equations 104
Chapter VII. Geometry of the Total Space of a Tangent Bundle 106
1. Non linear Connections in Tangent Bundle 106
2. Semisprays, Sprays and Non linear Connections 111
3. Torsions and Curvature of a Non linear Connections 115
4. Transformations of Non linear Connections 118
5. Normal d Connections on TM 121
6. Metrical Structures on TM 123
7. Some Remarkable Metrics on TM 126
Chapter VIII. Finsler Spaces 129
1. The Notion of Finsler Space 129
2. Non linear Cartan Connection 132
3. Geodesies 136
4. Metrical Cartan Connection 138
5. Structure Equations. Bianchi Identities 142
6. Remarkable Finslerian Connections 147
7. Almost Kahlerian Model of a Finsler Space 150
8. Subspaces in a Finsler Space 153
Chapter IX. Lagrange Spaces 157
1. The Notion of Lagrange Space 158
2. Euler Lagrange Equations. Canonical Non linear
Connection 160
3. Canonical Metrical d Connection 163
4. Gravitational and Electromagnetic Fields 166
5. Lagrange Space of Electrodynamics 170
6. Almost Finslerian Lagrange Spaces 173
7. Almost Kahlerian Model of a Lagrange Space 178
Chapter X. Generalized Lagrange Space 180
1. Notion of Generalized Lagrange Space 180
2. Metrical d Connections in a GL Space 183
3. Structure Equations. Parallelism 187
4. On h Covariant Constant d Tensor Fields 191
5. Gravitational Field 194
6. Electromagnetic Field 197
7. Almost Hermitian Model of a GLn Space 199
vii
Chapter XI. Applications of the GL Spaces with the Metric Tensor
e2ff(x y)7ij(x.y) 204
1. EPS conditions and the Metric e2 r(x yV(x) 204
2. Canonical Metrical d Connection 206
3. Electromagnetic and Gravitational Fields 210
4. Two Particular Cases 213
5. GLn Spaces with the Metric e2a(x yV(y) 214
6. Antonelli s Metrics 217
7. General Case 220
Chapter XII. Relativistic Geometrical Optics 223
1. Synge Metric in Dispersive Media 224
2. A Post Newtonian Estimation 225
3. A Non linear Connection 229
4. Canonical Metrical d Connection 233
5. Electromagnetic Tensors 236
6. Einstein Equations 238
7. Locally Minkowski GLn Spaces 241
8. Almost Hermitian Model 244
9. A Finslerian Approach to the Relativistic Optics 246
Chapter XIII. Geometry of Time Dependent Lagrangians 250
1. Non linear Connections in £ = (RxTM,7r,RxM) 250
2. Time Dependent Lagrangians 255
3. Non linear Connections and Semisprays 258
4. Normal d Connections on RXTM 260
5. Metrical Normal d Connections on RXTM 262
6. Rheonomic Finsler Spaces 265
7. Remarkable Time Dependent Lagrangians 268
8. Metrical Almost Contact Model of a Rheonomic Lagrange
Space 271
9. Generalized Rheonomic Lagrange Spaces 273
Bibliography 276
Index 284
|
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| language | English |
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| physical | XIV, 285 S. |
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| series | Fundamental theories of physics |
| series2 | Fundamental theories of physics |
| spelling | Miron, Radu Verfasser aut The geometry of Lagrange spaces theory and applications by Radu Miron and Mihai Anastasiei Dordrecht u.a. Kluwer 1994 XIV, 285 S. txt rdacontent n rdamedia nc rdacarrier Fundamental theories of physics 59 Géométrie différentielle ram Physique mathématique ram Mathematische Physik Geometry, Differential Lagrange spaces Mathematical physics Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Lagrange-Funktion (DE-588)4166459-0 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Lagrange-Funktion (DE-588)4166459-0 s Mannigfaltigkeit (DE-588)4037379-4 s DE-604 Differentialgeometrie (DE-588)4012248-7 s DE-188 Anastasiei, Mihai Verfasser aut Fundamental theories of physics 59 (DE-604)BV000012461 59 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006587975&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Miron, Radu Anastasiei, Mihai The geometry of Lagrange spaces theory and applications Fundamental theories of physics Géométrie différentielle ram Physique mathématique ram Mathematische Physik Geometry, Differential Lagrange spaces Mathematical physics Differentialgeometrie (DE-588)4012248-7 gnd Lagrange-Funktion (DE-588)4166459-0 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4166459-0 (DE-588)4037379-4 |
| title | The geometry of Lagrange spaces theory and applications |
| title_auth | The geometry of Lagrange spaces theory and applications |
| title_exact_search | The geometry of Lagrange spaces theory and applications |
| title_full | The geometry of Lagrange spaces theory and applications by Radu Miron and Mihai Anastasiei |
| title_fullStr | The geometry of Lagrange spaces theory and applications by Radu Miron and Mihai Anastasiei |
| title_full_unstemmed | The geometry of Lagrange spaces theory and applications by Radu Miron and Mihai Anastasiei |
| title_short | The geometry of Lagrange spaces |
| title_sort | the geometry of lagrange spaces theory and applications |
| title_sub | theory and applications |
| topic | Géométrie différentielle ram Physique mathématique ram Mathematische Physik Geometry, Differential Lagrange spaces Mathematical physics Differentialgeometrie (DE-588)4012248-7 gnd Lagrange-Funktion (DE-588)4166459-0 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd |
| topic_facet | Géométrie différentielle Physique mathématique Mathematische Physik Geometry, Differential Lagrange spaces Mathematical physics Differentialgeometrie Lagrange-Funktion Mannigfaltigkeit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006587975&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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