Tensor geometry: the geometric viewpoint and its uses
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1997
|
| Edition: | 2. ed., corr. 2. print. |
| Series: | Graduate texts in mathematics
130 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 432 S. Ill., graph. Darst. |
| ISBN: | 354052018X 9783540520184 |
Staff View
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Record in the Search Index
| _version_ | 1804125989758828544 |
|---|---|
| adam_text | C. T J. DODSON T. POSTON TENSOR GEOMETRY THE GEOMETRIC VIEWPOINT AND ITS
USES WITH 177 FIGURES SECOND EDITION SPRINGER CONTENTS INTRODUCTION XI
0. FUNDAMENTAL NOT(AT)IONS 1 1. SETS 1 2. FUNCTIONS 6 3. PHYSICAL
BACKGROUND 13 1. REAL VECTOR SPACES 18 1. SPACES 18 SUBSPACE GEOMETRY,
COMPONENTS 2. MAPS 24 LINEARITY, SINGULARITY, MATRICES 3. OPERATORS 31
PROJECTIONS, EIGENVALUES, DETERMINANT, TRACE II. AFFINE SPACES 43 1.
SPACES 43 TANGENT VECTORS, PARALLELISM, COORDINATES 2. COMBINATIONS OF
POINTS 49 MIDPOINTS, CONVEXITY 3. MAPS 53 LINEAR PARTS, TRANSLATIONS,
COMPONENTS III. DUAL SPACES 57 1. CONTOURS, CO- AND CONTRAVARIANCE, DUAL
BASIS 57 IV. METRIC VECTOR SPACES 64 1. METRICS 64 BASIC GEOMETRY AND
EXAMPLES, LORENTZ GEOMETRY 2. MAPS . 76 ISOMETRIES, ORTHOGONAL
PROJECTIONS AND COMPLEMENTS, ADJOINTS 3. COORDINATES 83 ORTHONORMAL
BASES VIII CONTENTS 4. DIAGONALISING SYMMETRIC OPERATORS 92 PRINCIPAL
DIRECTIONS, ISOTROPY V. TENSORS AND MULTILINEAR FORMS 98 1. MULTILINEAR
FORMS 98 TENSOR PRODUCTS, DEGREE, CONTRACTION, RAISING INDICES VI;
TOPOLOGICAL VECTOR SPACES 114 1. CONTINUITY 114 METRICS, TOPOLOGIES,
HOMEOMORPHISMS 2. LIMITS 125 CONVERGENCE AND CONTINUITY 3. THE USUAL
TOPOLOGY 128 CONTINUITY IN FINITE DIMENSIONS 4. COMPACTNESS AND
COMPLETENESS 136 INTERMEDIATE VALUE THEOREM, CONVERGENCE, EXTREMA VII.
DIFFERENTIATION AND MANIFOLDS 149 1. DIFFERENTIATION , 149 DERIVATIVE AS
LOCAL LINEAR APPROXIAMATION 2. MANIFOLDS 160 CHARTS, MAPS,
DIFFEOMORPHISMS 3. BUNDLES AND FIELDS 170 TANGENT AND TENSOR BUNDLES,
METRIC TENSORS 4. COMPONENTS 182 HAIRY BALL THEOREM, TRANSFORMATION
FORMULAE, RAISING INDICES 5. CURVES 189 PARAMETRISATION, LENGTH,
INTEGRATION 6. VECTOR FIELDS AND FLOWS 195 FIRST ORDER ORDINARY
DIFFERENTIAL EQUATIONS 7. LIE BRACKETS 200 COMMUTING VECTOR FIELDS AND
FLOWS VIII. CONNECTIONS AND COVARIANT DIFFERENTIATION 205 1. CURVES AND
TANGENT VECTORS 205 REPRESENTING A VECTOR BY A CURVE 2. ROLLING WITHOUT
TURNING 207 DIFFERENTIATION ALONG CURVES IN EMBEDDED MANIFOLDS 3.
DIFFERENTIATING SECTIONS 212 CONNECTIONS, HORIZONTAL VECTORS,
CHRISTOFFEL SYMBOLS 4. PARALLEL TRANSPORT 222 INTEGRATING A CONNECTION
CONTENTS IX 5. TORSION AND SYMMETRY 228 TORSION TENSOR OF A CONNECTION
6. METRIC TENSORS AND CONNECTIONS 232 LEVI-CIVITA CONNECTION 7.
COVARIANT DIFFERENTIATION OF TENSORS 240 PARALLEL TRANSPORT, RICCI S
LEMMA, COMPONENTS, CONSTANCY IX. GEODESIES 246 1. LOCAL CHARACTERISATION
246 UNDEVIATING CURVES 2. GEODESIES FROM A POINT 249 COMPLETENESS,
EXPONENTIAL MAP, NORMAL COORDINATES 3. GLOBAL CHARACTERISATION 256
CRITICALITY OF LENGTH AND ENERGY, FIRST VARIATION FORMULA 4. MAXIMA,
MINIMA, UNIQUENESS 264 SADDLE POINTS, MIRAGES, TWINS PARADOX 5.
GEODESIES IN EMBEDDED MANIFOLDS 275 CHARACTERISATION, EXAMPLES 6. AN
EXAMPLE OF LIE GROUP GEOMETRY 281 2X2 MATRICES AS A PSEUDO-RIEMANNIAN
MANIFOLD X. CURVATURE 298 1. FLAT SPACES 298 INTRINSIC DESCRIPTION OF
LOCAL FLATNESS 2. THE CURVATURE TENSOR 304 PROPERTIES AND COMPONENTS 3.
CURVED SURFACES 319 GAUSSIAN CURVATURE, GAUSS-BONNET THEOREM 4. GEODESIC
DEVIATION 324 TIDAL EFFECTS IN SPACETIME 5. SECTIONAL CURVATURE 326
SCHUR S THEOREM, CONSTANT CURVATURE 6. RICCI AND EINSTEIN TENSORS 329
SIGNS, GEOMETRY, EINSTEIN MANIFOLDS, CONSERVATION EQUATION 7. THE WEYL
TENSOR 337 XI. SPECIAL RELATIVITY 340 1. ORIENTING SPACETIMES 340
CAUSALITY, PARTICLE HISTORIES 2. MOTION IN FLAT SPACETIME 342 INERTIAL
FRAMES, MOMENTUM, REST MASS, MASS-ENERGY 3. FIELDS 355 MATTER TENSOR,
CONSERVATION X CONTENTS 4. FORCES 367 NO SCALAR POTENTIALS 5.
GRAVITATIONAL RED SHIFT AND CURVATURE 369 MEASUREMENT GIVES A CURVED
METRIC TENSOR XII. GENERAL RELATIVITY 372 1. HOW GEOMETRY GOVERNS MATTER
372 EQUIVALENCE PRINCIPLE, FREE FALL 2. WHAT MATTER DOES TO GEOMETRY 377
EINSTEIN S EQUATION, SHAPE OF SPACETIME 3. THE STARS IN THEIR COURSES
384 GEOMETRY OF THE SOLAR SYSTEM, SCHWARZSCHILD SOLUTION 4. FAREWELL
PARTICLE 398 APPENDIX. EXISTENCE AND SMOOTHNESS OF FLOWS 400 1.
COMPLETENESS 400 2. TWO FIXED POINT THEOREMS 401 3. SEQUENCES OF
FUNCTIONS 404 4. INTEGRATING VECTOR QUANTITIES 408 5. THE MAIN PROOF 408
6. INVERSE FUNCTION THEOREM 415 BIBLIOGRAPHY 418 INDEX OF NOTATIONS 421
INDEX 424
|
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| author | Dodson, Christopher T. J. 1941- Poston, Timothy |
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| author_sort | Dodson, Christopher T. J. 1941- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
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| dewey-search | 516.3/6 |
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| discipline | Mathematik |
| edition | 2. ed., corr. 2. print. |
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| indexdate | 2024-07-09T18:10:19Z |
| institution | BVB |
| isbn | 354052018X 9783540520184 |
| language | English |
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| spelling | Dodson, Christopher T. J. 1941- Verfasser (DE-588)12958472X aut Tensor geometry the geometric viewpoint and its uses C. T. J. Dodson ; T. Poston 2. ed., corr. 2. print. Berlin [u.a.] Springer 1997 XIV, 432 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 130 Calculus of tensors Geometry, Differential Tensorrechnung (DE-588)4192487-3 gnd rswk-swf Tensor (DE-588)4184723-4 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Tensorrechnung (DE-588)4192487-3 s Differentialgeometrie (DE-588)4012248-7 s DE-604 Tensor (DE-588)4184723-4 s 1\p DE-604 Poston, Timothy Verfasser aut Graduate texts in mathematics 130 (DE-604)BV000000067 130 SWBplus Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007716908&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Dodson, Christopher T. J. 1941- Poston, Timothy Tensor geometry the geometric viewpoint and its uses Graduate texts in mathematics Calculus of tensors Geometry, Differential Tensorrechnung (DE-588)4192487-3 gnd Tensor (DE-588)4184723-4 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4192487-3 (DE-588)4184723-4 (DE-588)4012248-7 |
| title | Tensor geometry the geometric viewpoint and its uses |
| title_auth | Tensor geometry the geometric viewpoint and its uses |
| title_exact_search | Tensor geometry the geometric viewpoint and its uses |
| title_full | Tensor geometry the geometric viewpoint and its uses C. T. J. Dodson ; T. Poston |
| title_fullStr | Tensor geometry the geometric viewpoint and its uses C. T. J. Dodson ; T. Poston |
| title_full_unstemmed | Tensor geometry the geometric viewpoint and its uses C. T. J. Dodson ; T. Poston |
| title_short | Tensor geometry |
| title_sort | tensor geometry the geometric viewpoint and its uses |
| title_sub | the geometric viewpoint and its uses |
| topic | Calculus of tensors Geometry, Differential Tensorrechnung (DE-588)4192487-3 gnd Tensor (DE-588)4184723-4 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Calculus of tensors Geometry, Differential Tensorrechnung Tensor Differentialgeometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007716908&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000067 |
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