Symmetries and curvature structure in general relativity /
Hall (U. of Aberdeen) compiles the theoretical aspects of the literature on symmetries in general relativity that have been produced over the past few decades. He is not offering a textbook, he warns, but a study of certain aspects of four-dimensional Lorentzian differential geometry emphasizing the...
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| Corporate Author: | |
| Format: | Book |
| Language: | English |
| Published: |
River Edge, N.J. ; London :
World Scientific,
c2004
River Edge, NJ : [2004], ©2004 River Edge, NJ : c2004 River Edge, N.J. : [2004] |
| Series: | World Scientific lecture notes in physics ;
v. 46 World Scientific lecture notes in physics v. 46 World Scientific lecture notes in physics ; v. 46 |
| Subjects: |
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| 100 | 1 | |a Hall, G. S |q (Graham S.) |0 http://viaf.org/viaf/74004990 | |
| 100 | 1 | |a Hall, G. S |q (Graham S.) |1 http://viaf.org/viaf/74004990 | |
| 100 | 1 | |a Hall, G. S |q (Graham S.) | |
| 245 | 1 | 0 | |a Symmetries and curvature structure in general relativity / |c G.S. Hall |
| 260 | |a River Edge, N.J. ; |a London : |b World Scientific, |c c2004 | ||
| 260 | |a River Edge, NJ : |b World Scientific, |c [2004], ©2004 | ||
| 260 | |a River Edge, NJ : |b World Scientific, |c c2004 | ||
| 264 | 1 | |a River Edge, N.J. : |b World Scientific, |c [2004] | |
| 264 | 4 | |c ©2004 | |
| 300 | |a x, 430 p. : |b ill. ; |c 24 cm | ||
| 300 | |a x, 430 pages : |b illustrations ; |c 24 cm | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a unmediated |b n |2 rdamedia | ||
| 338 | |a volume |b nc |2 rdacarrier | ||
| 440 | 0 | |a World Scientific lecture notes in physics ; |v v. 46 | |
| 440 | 0 | |a World Scientific lecture notes in physics |v v. 46 | |
| 490 | 1 | |a World Scientific lecture notes in physics ; |v v. 46 | |
| 500 | |a This WorldCat-derived record is shareable under Open Data Commons ODC-BY, with attribution to OCLC |5 CTY | ||
| 504 | |a Includes bibliographical references (p. 413-420) and index | ||
| 504 | |a Includes bibliographical references (pages 413-420) and index | ||
| 505 | 0 | 0 | |g 1 |t Introduction -- |g 2. |t Algebraic concepts -- |g 3. |t Topology -- |g 4. |t Manifold theory -- |g 5. |t Lie groups -- |g 6. |t The Lorentz group -- |g 7. |t Space-times and algebraic classification -- |g 8. |t Holonomy groups and general relativity -- |g 9. |t The connection and curvature structure of space-time -- |g 10. |t Affine vector fields on space-time -- |g 11. |t Conformal symmetry in space-times -- |g 12. |t Projective symmetry in space-times -- |g 13. |t Curvature collineations. |
| 505 | 0 | 0 | |g 1 |t Introduction -- |g 2. |t Algebraic concepts -- |g 3. |t Topology -- |g 4. |t Manifold theory -- |g 5. |t Lie groups -- |g 6. |t The Lorentz group -- |g 7. |t Space-times and algebraic classification -- |g 8. |t Holonomy groups and general relativity -- |g 9. |t The connection and curvature structure of space-time -- |g 10. |t Affine vector fields on space-time -- |g 11. |t Conformal symmetry in space-times -- |g 12. |t Projective symmetry in space-times -- |g 13. |t Curvature collineations. |
| 505 | 0 | 0 | |g 1.1 |t Geometry and Physics |g 1 -- |g 1.2 |t Preview of Future Chapters |g 5 -- |g 2 |t Algebraic Concepts |g 11 -- |g 2.2 |t Groups |g 11 -- |g 2.3 |t Vector Spaces |g 15 -- |g 2.4 |t Dual Spaces |g 22 -- |g 2.5 |t Forms and Inner Products |g 23 -- |g 2.6 |t Similarity, Jordan Canonical Forms and Segre Types |g 28 -- |g 2.7 |t Lie Algebras |g 38 -- |g 3 |t Topology |g 41 -- |g 3.2 |t Metric Spaces |g 42 -- |g 3.3 |t Topological Spaces |g 45 -- |g 3.4 |t Bases |g 49 -- |g 3.5 |t Subspace Topology |g 51 -- |g 3.6 |t Quotient Spaces |g 52 -- |g 3.7 |t Product Spaces |g 53 -- |g 3.8 |t Compactness and Paracompactness |g 53 -- |g 3.9 |t Connected Spaces |g 56 -- |g 3.10 |t Covering Spaces and the Fundamental Group |g 58 -- |g 3.11 |t The Rank Theorems |g 61 -- |g 4 |t Manifold Theory |g 63 -- |g 4.2 |t Calculus on R[superscript n] |g 64 -- |g 4.3 |t Manifolds |g 65 -- |g 4.4 |t Functions on Manifolds |g 68 -- |g 4.5 |t The Manifold Topology |g 70 -- |g 4.6 |t The Tangent Space and Tangent Bundle |g 73 -- |g 4.7 |t Tensor Spaces and Tensor Bundles |g 75 -- |g 4.8 |t Vector and Tensor Fields |g 77 -- |g 4.9 |t Derived Maps and Pullbacks |g 81 -- |g 4.10 |t Integral Curves of Vector Fields |g 83 -- |g 4.11 |t Submanifolds |g 85 -- |g 4.12 |t Quotient Manifolds |g 92 -- |g 4.13 |t Distributions |g 92 -- |g 4.14 |t Curves and Coverings |g 97 -- |g 4.15 |t Metrics on Manifolds |g 99 -- |g 4.16 |t Linear Connections and Curvature |g 104 -- |g 4.17 |t Grassmann and Stiefel Manifolds |g 116 -- |g 5 |t Lie Groups |g 119 -- |g 5.1 |t Topological Groups |g 119 -- |g 5.2 |t Lie Groups |g 121 -- |g 5.3 |t Lie Subgroups |g 122 -- |g 5.4 |t Lie Algebras |g 124 -- |g 5.5 |t One Parameter Subgroups and the Exponential Map |g 127 -- |g 5.6 |t Transformation Groups |g 131 -- |g 5.7 |t Lie Transformation Groups |g 131 -- |g 5.8 |t Orbits and Isotropy Groups |g 133 -- |g 5.9 |t Complete Vector Fields |g 135 -- |g 5.10 |t Groups of Transformations |g 138 -- |g 5.11 |t Local Group Actions |g 140 -- |g 5.12 |t Lie Algebras of Vector Fields |g 142 -- |g 5.13 |t The Lie Derivative |g 144 -- |g 6 |t The Lorentz Group |g 147 -- |g 6.1 |t Minkowski Space |g 147 -- |g 6.2 |t The Lorentz Group |g 150 -- |g 6.3 |t The Lorentz Group as a Lie Group |g 158 -- |g 6.4 |t The Connected Lie Subgroups of the Lorentz Group |g 163 -- |g 7 |t Space-Times and Algebraic Classification |g 169 -- |g 7.1.1 |t Electromagnetic fields |g 171 -- |g 7.1.2 |t Fluid Space-Times |g 172 -- |g 7.1.3 |t The Vacuum Case |g 172 -- |g 7.2 |t Bivectors and their Classification |g 173 -- |g 7.3 |t The Petrov Classification |g 184 -- |g 7.4 |t Alternative Approaches to the Petrov Classification |g 191 -- |g 7.5 |t The Classification of Second Order Symmetric Tensors |g 202 -- |g 7.6 |t The Anti-Self Dual Representation of Second Order Symmetric Tensors |g 208 -- |g 7.7 |t Examples and Applications |g 215 -- |g 7.8 |t The Local and Global Nature of Algebraic Classifications |g 221 -- |g 8 |t Holonomy Groups and General Relativity |g 227 -- |g 8.3 |t The Holonomy Group of a Space-Time |g 234 -- |g 8.4 |t Vacuum Space-Times |g 245 -- |g 9 |t The Connection and Curvature Structure of Space-Time |g 255 -- |g 9.2 |t Metric and Connection |g 255 -- |g 9.3 |t Metric, Connection and Curvature |g 259 -- |g 9.4 |t Sectional Curvature |g 270 -- |g 9.5 |t Retrospect |g 282 -- |g 10 |t Affine Vector Fields on Space-Time |g 285 -- |g 10.1 |t General Aspects of Symmetries |g 285 -- |g 10.3 |t Subalgebras of the Affine Algebra; Isometries and Homotheties |g 291 -- |g 10.4 |t Fixed Point Structure |g 296 -- |g 10.5 |t Orbit Structure |g 311 -- |g 10.6 |t Space-Times admitting Proper Affine Vector Fields |g 323 -- |g 10.7 |t Examples and Summary |g 333 -- |g 11 |t Conformal Symmetry in Space-times |g 341 -- |g 11.1 |t Conformal Vector Fields |g 341 -- |g 11.2 |t Orbit Structure |g 345 -- |g 11.3 |t Fixed Point Structure |g 349 -- |g 11.4 |t Conformal Reduction of the Conformal Algebra |g 352 -- |g 11.5 |t Conformal Vector Fields in Vacuum Space-Times |g 358 -- |g 11.7 |t Special Conformal Vector Fields |g 363 -- |g 12 |t Projective Symmetry in Space-times |g 371 -- |g 12.1 |t Projective Vector Fields |g 371 -- |g 12.2 |t General Theorems on Projective Vector Fields |g 375 -- |g 12.3 |t Space-Times Admitting Projective Vector Fields |g 381 -- |g 12.4 |t Special Projective Vector Fields |g 389 -- |g 12.5 |t Projective Symmetry and Holonomy |g 391 -- |g 13 |t Curvature Collineations |g 397 -- |g 13.3 |t Some Techniques for Curvature Collineations |g 400 |
| 520 | |a Hall (U. of Aberdeen) compiles the theoretical aspects of the literature on symmetries in general relativity that have been produced over the past few decades. He is not offering a textbook, he warns, but a study of certain aspects of four-dimensional Lorentzian differential geometry emphasizing the special requirements of Einstein's general theory of relativity. His main goal is to present a mathematical approach to symmetries and to the related topic of the connection and curvature structure of space-time, without paying much attention to attendant problems that worry mathematicians more than physicists. Annotation ©2004 Book News, Inc., Portland, OR (booknews.com) | ||
| 590 | |a *lll 20060315 | ||
| 590 | |a Acquired for the Penn Libraries with assistance from the Class of 1932 Fund | ||
| 596 | |a 31 | ||
| 650 | 0 | |a Relativity (Physics) | |
| 650 | 0 | |a Spaces of constant curvature | |
| 650 | 0 | |a Symmetric spaces | |
| 650 | 0 | |a Symmetry (Physics) | |
| 650 | 7 | |a Relativity (Physics) |2 fast | |
| 650 | 7 | |a Spaces of constant curvature |2 fast | |
| 650 | 7 | |a Symmetric spaces |2 fast | |
| 650 | 7 | |a Symmetry (Physics) |2 fast | |
| 710 | 2 | |a Class of 1932 Fund |5 PU | |
| 830 | 0 | |a World Scientific lecture notes in physics ; |v v. 46 | |
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