Verfügbarkeit: Tensor geometry | Technische Universität München

Tensor geometry: the geometric viewpoint and its uses

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Bibliographische Detailangaben
Beteiligte Personen:	Dodson, Christopher T. J. 1941- (VerfasserIn), Poston, Timothy (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Berlin [u.a.] Springer 1997
Ausgabe:	2. ed., corr. 2. print.
Schriftenreihe:	Graduate texts in mathematics 130
Schlagwörter:	Calculus of tensors Geometry, Differential Tensorrechnung Tensor Differentialgeometrie
Links:	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
Umfang:	XIV, 432 S. Ill., graph. Darst.
ISBN:	354052018X 9783540520184

Internformat

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Datensatz im Suchindex

DE-BY-TUM_call_number	0202 MAT 530f 2007 A 6476(2,1997)
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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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isbn	354052018X 9783540520184
language	English
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series	Graduate texts in mathematics
series2	Graduate texts in mathematics
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
work_keys_str_mv	AT dodsonchristophertj tensorgeometrythegeometricviewpointanditsuses AT postontimothy tensorgeometrythegeometricviewpointanditsuses

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