Analysis and algebra on differentiable manifolds: a workbook for students and teachers
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
2001
|
| Series: | Kluwer texts in the mathematical sciences
23 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | CD-ROM u.d.T.: Superficies / Angel Montesinos |
| Physical Description: | XVII, 478 S. Ill., graph. Darst. CD-ROM (12 cm) |
| ISBN: | 1402000278 1402001630 9781402001635 9781402000270 |
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MARC
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Record in the Search Index
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| adam_text | ANALYSIS AND ALGEBRA ON DIFFERENTIABLE MANIFOLDS: A WORKBOOK FOR
STUDENTS AND TEACHERS BY P.M. GADEA AND J. MUNOZ MASQUE CONSEJO SUPERIOR
DE INVESTIGACIONES CIENTIFICAS, INSTITUTE DE FISICA APLICADA,
DEPARTAMENTO DE TRATAMIENTO DE LA INFORMATION Y CODIFICATION, MADRID,
SPAIN KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON /.IIONDON CONTENTS
PROLOGUE XI PREFACE XIII ACKNOWLEDGMENTS XV ABOUT THE AUTHORS XVII 1.
DIFFERENTIABLE MANIFOLDS 1 1.1 C MANIFOLDS 1 1.2 DIFFERENTIABLE
STRUCTURES DENNED ON SETS 14 1.3 DIFFERENTIABLE FUNCTIONS AND MAPPINGS
24 1.4 CRITICAL POINTS AND VALUES 29 1.5 IMMERSIONS, SUBMANIFOLDS,
EMBEDDINGS, AND DIFFEOMORPHISMS 33 1.6 CONSTRUCTING MANIFOLDS BY INVERSE
IMAGE. IMPLICIT MAP THEOREM 43 1.7 SUBMERSIONS. QUOTIENT MANIFOLDS 48
1.8 THE TANGENT BUNDLE 57 1.9 VECTOR FIELDS 61 1.9.1 WORKING WITH VECTOR
FIELDS 61 1.9.2 INTEGRAL CURVES 68 1.9.3 FLOWS 72 1.9.4 TRANSFORMING
VECTOR FIELDS 75 2. TENSOR FIELDS AND DIFFERENTIAL FORMS 79 2.1 VECTOR
BUNDLES 79 2.2 TENSOR AND EXTERIOR ALGEBRAS. TENSOR FIELDS 86 2.3
DIFFERENTIAL FORMS. EXTERIOR PRODUCT 88 2.4 LIE DERIVATIVE. INTERIOR
PRODUCT 97 2.5 DISTRIBUTIONS AND INTEGRAL MANIFOLDS. FROBENIUS THEOREM.
DIFFERENTIAL IDEALS. 102 2.6 ALMOST SYMPLECTIC MANIFOLDS 110 3.
INTEGRATION ON MANIFOLDS 119 VII VIII ANALYSIS AND ALGEBRA ON
DIFFERENTIABLE MANIFOLDS 3.1 ORIENTABLE MANIFOLDS.
ORIENTATION-PRESERVING MAPS 119 3.2 INTEGRATION ON CHAINS. STOKES
THEOREM I 123 3.3 INTEGRATION ON ORIENTED MANIFOLDS. STOKES THEOREM II
125 3.4 DE RHAM COHOMOLOGY 129 4. LIE GROUPS 137 4.1 LIE GROUPS AND LIE
ALGEBRAS 137 4.2 HOMOMORPHISMS OF LIE GROUPS AND LIE ALGEBRAS 150 4.3
LIE SUBGROUPS AND LIE SUBALGEBRAS 155 4.4 THE EXPONENTIAL MAP 164 4.5
THE ADJOINT REPRESENTATION 170 4.6 LIE GROUPS OF TRANSFORMATIONS 178 4.7
HOMOGENEOUS SPACES 186 5. FIBRE BUNDLES 197 5.1 PRINCIPAL BUNDLES 197
5.2 CONNECTIONS IN BUNDLES 206 5.3 CHARACTERISTIC CLASSES 211 5.4 LINEAR
CONNECTIONS 225 5.5 TORSION AND CURVATURE 228 5.6 GEODESIES 236 5.7
ALMOST COMPLEX MANIFOLDS 239 6. RIEMANNIAN GEOMETRY 249 6.1 RIEMANNIAN
MANIFOLDS 249 6.2 RIEMANNIAN CONNECTIONS 254 6.3 GEODESIES 259 6.4 THE
EXPONENTIAL MAP 265 6.5 CURVATURE AND RICCI TENSORS 269 6.6
CHARACTERISTIC CLASSES 272 6.7 ISOMETRIES 277 6.8 HOMOGENEOUS RIEMANNIAN
MANIFOLDS AND RIEMANNIAN SYMMETRIC SPACES 284 6.9 SPACES OF CONSTANT
CURVATURE 293 6.10 LEFT-INVARIANT METRICS ON LIE GROUPS 297 6.11
GRADIENT, DIVERGENCE, CODIFFERENTIAL, CURL, LAPLACIAN, AND HODGE STAR
OPERATOR ON RIEMANNIAN MANIFOLDS 305 6.12 AFFINE, KILLING, CONFORMAL,
PROJECTIVE, JACOBI, HARMONIC VECTOR FIELDS 318 6.13 SUBMANIFOLDS. SECOND
FUNDAMENTAL FORM 333 6.14 SURFACES IN IR 3 339 6.15 PSEUDO-RIEMANNIAN
MANIFOLDS 347 7. SOME DEFINITIONS AND THEOREMS 373 7.1 CHAPTER 1.
DIFFERENTIABLE MANIFOLDS 373 CONTENTS IX 7.2 CHAPTER 2. TENSOR FIELDS.
DIFFERENTIAL FORMS 379 7.3 CHAPTER 3. INTEGRATION ON MANIFOLDS 383 7.4
CHAPTER 4. LIE GROUPS 385 7.5 CHAPTER 5. FIBRE BUNDLES 391 7.6 CHAPTER
6. RIEMANNIAN GEOMETRY 396 8. SOME FORMULAS AND TABLES 403 9. MANUAL
OF SUPERFICIES 447 10.INDICES AND NOTATIONS 455 REFERENCES 457 LIST OF
NOTATIONS 461 LIST OF FIGURES 465 INDEX 467
|
| any_adam_object | 1 |
| author | Gadea, Pedro M. Muñoz Masqué, Jaime 1950- |
| author_GND | (DE-588)141048573 (DE-588)14104862X |
| author_facet | Gadea, Pedro M. Muñoz Masqué, Jaime 1950- |
| author_role | aut aut |
| author_sort | Gadea, Pedro M. |
| author_variant | p m g pm pmg m j m mj mjm |
| building | Verbundindex |
| bvnumber | BV015635477 |
| callnumber-first | Q - Science |
| callnumber-label | QA614 |
| callnumber-raw | QA614.3 |
| callnumber-search | QA614.3 |
| callnumber-sort | QA 3614.3 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 220 |
| ctrlnum | (OCoLC)48628522 (DE-599)BVBBV015635477 |
| dewey-full | 516.3/6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/6 |
| dewey-search | 516.3/6 |
| dewey-sort | 3516.3 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV015635477 |
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| indexdate | 2024-07-09T19:09:27Z |
| institution | BVB |
| isbn | 1402000278 1402001630 9781402001635 9781402000270 |
| language | English |
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| owner_facet | DE-824 DE-83 DE-11 |
| physical | XVII, 478 S. Ill., graph. Darst. CD-ROM (12 cm) |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Kluwer |
| record_format | marc |
| series | Kluwer texts in the mathematical sciences |
| series2 | Kluwer texts in the mathematical sciences |
| spelling | Gadea, Pedro M. Verfasser (DE-588)141048573 aut Analysis and algebra on differentiable manifolds a workbook for students and teachers by P. M. Gadea and J. Muñoz Masqué Superficies Dordrecht [u.a.] Kluwer 2001 XVII, 478 S. Ill., graph. Darst. CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Kluwer texts in the mathematical sciences 23 CD-ROM u.d.T.: Superficies / Angel Montesinos Variétés différentiables Differentiable manifolds Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf CD-ROM (DE-588)4139307-7 gnd rswk-swf Algebra (DE-588)4001156-2 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Algebra (DE-588)4001156-2 s CD-ROM (DE-588)4139307-7 s DE-604 Analysis (DE-588)4001865-9 s Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 s 1\p DE-604 Muñoz Masqué, Jaime 1950- Verfasser (DE-588)14104862X aut Montesinos, Angel Sonstige oth Kluwer texts in the mathematical sciences 23 (DE-604)BV005450041 23 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010115765&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 | Gadea, Pedro M. Muñoz Masqué, Jaime 1950- Analysis and algebra on differentiable manifolds a workbook for students and teachers Kluwer texts in the mathematical sciences Variétés différentiables Differentiable manifolds Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd Analysis (DE-588)4001865-9 gnd CD-ROM (DE-588)4139307-7 gnd Algebra (DE-588)4001156-2 gnd |
| subject_GND | (DE-588)4012269-4 (DE-588)4001865-9 (DE-588)4139307-7 (DE-588)4001156-2 (DE-588)4151278-9 |
| title | Analysis and algebra on differentiable manifolds a workbook for students and teachers |
| title_alt | Superficies |
| title_auth | Analysis and algebra on differentiable manifolds a workbook for students and teachers |
| title_exact_search | Analysis and algebra on differentiable manifolds a workbook for students and teachers |
| title_full | Analysis and algebra on differentiable manifolds a workbook for students and teachers by P. M. Gadea and J. Muñoz Masqué |
| title_fullStr | Analysis and algebra on differentiable manifolds a workbook for students and teachers by P. M. Gadea and J. Muñoz Masqué |
| title_full_unstemmed | Analysis and algebra on differentiable manifolds a workbook for students and teachers by P. M. Gadea and J. Muñoz Masqué |
| title_short | Analysis and algebra on differentiable manifolds |
| title_sort | analysis and algebra on differentiable manifolds a workbook for students and teachers |
| title_sub | a workbook for students and teachers |
| topic | Variétés différentiables Differentiable manifolds Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd Analysis (DE-588)4001865-9 gnd CD-ROM (DE-588)4139307-7 gnd Algebra (DE-588)4001156-2 gnd |
| topic_facet | Variétés différentiables Differentiable manifolds Differenzierbare Mannigfaltigkeit Analysis CD-ROM Algebra Einführung |
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