An introduction to differentiable manifolds and Riemannian geometry:
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Amsterdam ; London ; New York ; Oxford ; Paris ; Tokyo ; Boston ; San Diego ; San Francisco ; Singapore ; Sydney
Academic Press
[2003]
|
| Edition: | revised second edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverzeichnis: Seite 403 - 409 Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | xiv, 419 Seiten Illustrationen, Diagramme |
| ISBN: | 9780121160517 0121160513 |
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MARC
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| 100 | 1 | |a Boothby, William M. |d 1918- |0 (DE-588)171984412 |4 aut | |
| 245 | 1 | 0 | |a An introduction to differentiable manifolds and Riemannian geometry |c William M. Boothby |
| 250 | |a revised second edition | ||
| 264 | 1 | |a Amsterdam ; London ; New York ; Oxford ; Paris ; Tokyo ; Boston ; San Diego ; San Francisco ; Singapore ; Sydney |b Academic Press |c [2003] | |
| 264 | 4 | |c © 2003 | |
| 300 | |a xiv, 419 Seiten |b Illustrationen, Diagramme | ||
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| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverzeichnis: Seite 403 - 409 | ||
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 7 | |a Geometria diferencial |2 larpcal | |
| 650 | 7 | |a Geometria riemanniana |2 larpcal | |
| 650 | 7 | |a Variedades diferenciáveis |2 larpcal | |
| 650 | 4 | |a Differentiable manifolds | |
| 650 | 4 | |a Riemannian manifolds | |
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Record in the Search Index
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| adam_text |
AN INTRODUCTION TO DIFFERENTIABLE MANIFOLDS AND RIEMANNIAN GEOMETRY
REVISED SECOND EDITION WILLIAM M. BOOTHBY WASHINGTON UNIVERSITY ST.
LOUIS, MISSOURI ACADEMIC PRESS AN IMPRINT OF ELSEVIER SCIENCE AMSTERDAM
BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO
SINGAPORE SYDNEY TOKYO CONTENTS PREFACE TO THE REVISED SECOND EDITION XI
PREFACE TO THE SECOND EDITION XIII PREFACE TO THE FIRST EDITION XV I.
INTRODUCTION TO MANIFOLDS 1. PRELIMINARY COMMENTS ON R" 1 2. R" AND
EUCLIDEAN SPACE , 4 3. TOPOLOGICAL MANIFOLDS 6 4. FURTHER EXAMPLES OF
MANIFOLDS. CUTTING AND PASTING 11 5. ABSTRACT MANIFOLDS. SOME EXAMPLES
14 II. FUNCTIONS OF SEVERAL VARIABLES AND MAPPINGS 1. DIFFERENTIABILITY
FOR FUNCTIONS OF SEVERAL VARIABLES 20 2. DIFFERENTIABILITY OF MAPPINGS
AND JACOBIANS 25 3. THE SPACE OF TANGENT VECTORS AT A POINT OF R" 29 4.
ANOTHER DEFINITION OF T A {R) 32 5. VECTOR FIELDS ON OPEN SUBSETS OF R"
36 6. THE INVERSE FUNCTION THEOREM 41 7. THE RANK OF A MAPPING 46 III.
DIFFERENTIABLE MANIFOLDS AND SUBMANIFOLDS 1. THE DEFINITION OF A
DIFFERENTIABLE MANIFOLD 52 2. FURTHER EXAMPLES 59 3. DIFFERENTIABLE
FUNCTIONS AND MAPPINGS 65 4. RANK OF A MAPPING, IMMERSIONS 68 5.
SUBMANIFOLDS 74 6. LIE GROUPS 80 7. THE ACTION OF A LIE GROUP ON A
MANIFOLD. TRANSFORMATION GROUPS 87 8. THE ACTION OF A DISCRETE GROUP ON
A MANIFOLD 93 9. COVERING MANIFOLDS 98 VII VIII CONTENTS IV. VECTOR
FIELDS ON A MANIFOLD 1. THE TANGENT SPACE AT A POINT OF A MANIFOLD 104
2. VECTOR FIELDS 113 3. ONE-PARAMETER AND LOCAL ONE-PARAMETER GROUPS
ACTING ON A MANIFOLD 119 4. THE EXISTENCE THEOREM FOR ORDINARY
DIFFERENTIAL EQUATIONS 127 5. SOME EXAMPLES OF ONE-PARAMETER GROUPS
ACTING ON A MANIFOLD 135 6. ONE-PARAMETER SUBGROUPS OF LIE GROUPS 142 7.
THE LIE ALGEBRA OF VECTOR FIELDS ON A MANIFOLD 146 8. FROBENIUS'S
THEOREM 153 9. HOMOGENEOUS SPACES 160 V. TENSORS AND TENSOR FIELDS ON
MANIFOLDS 1. TANGENT COVECTORS 171 COVECTORS ON MANIFOLDS 172 COVECTOR
FIELDS AND MAPPINGS 174 2. BILINEAR FORMS. THE RIEMANNIAN METRIC 177 3.
RIEMANNIAN MANIFOLDS AS METRIC SPACES 181 4. PARTITIONS OF UNITY 186
SOME APPLICATIONS OF THE PARTITION OF UNITY 188 5. TENSOR FIELDS 192
TENSORS ON A VECTOR SPACE 192 TENSOR FIELDS 194 MAPPINGS AND COVARIANT
TENSORS 195 THE SYMMETRIZING AND ALTERNATING TRANSFORMATIONS 196 6.
MULTIPLICATION OF TENSORS 199 MULTIPLICATION OF TENSORS ON A VECTOR
SPACE 199 MULTIPLICATION OF TENSOR FIELDS 201 EXTERIOR MULTIPLICATION OF
ALTERNATING TENSORS 202 THE EXTERIOR ALGEBRA ON MANIFOLDS 206 7.
ORIENTATION OF MANIFOLDS AND THE VOLUME ELEMENT 207 8. EXTERIOR
DIFFERENTIATION 212 AN APPLICATION TO FROBENIUS'S THEOREM 216 VI.
INTEGRATION ON MANIFOLDS 1. INTEGRATION IN R" DOMAINS OF INTEGRATION 223
BASIC PROPERTIES OF THE RIEMANN INTEGRAL 224 2. A GENERALIZATION TO
MANIFOLDS 229 INTEGRATION ON RIEMANNIAN MANIFOLDS 232 3. INTEGRATION ON
LIE GROUPS 237 4. MANIFOLDS WITH BOUNDARY 243 5. STOKES'S THEOREM FOR
MANIFOLDS 251 6. HOMOTOPY OF MAPPINGS. THE FUNDAMENTAL GROUP 258
HOMOTOPY OF PATHS AND LOOPS. THE FUNDAMENTAL GROUP 259 CONTENTS 7. SOME
APPLICATIONS OF DIFFERENTIAL FORMS. THE DE RHAM GROUPS 265 THE HOMOTOPY
OPERATOR 268 8. SOME FURTHER APPLICATIONS OF DE RHAM GROUPS 272 THE DE
RHAM GROUPS OF LIE GROUPS 276 9. COVERING SPACES AND FUNDAMENTAL GROUP
280 VII. DIFFERENTIATION ON RIEMANNIAN MANIFOLDS 1. DIFFERENTIATION OF
VECTOR FIELDS ALONG CURVES IN R " 289 THE GEOMETRY OF SPACE CURVES 292
CURVATURE OF PLANE CURVES 296 2. DIFFERENTIATION OF VECTOR FIELDS ON
SUBMANIFOLDS OF R" 298 FORMULAS FOR COVARIANT DERIVATIVES 303 V^ Y AND
DIFFERENTIATION OF VECTOR FIELDS 305 3. DIFFERENTIATION ON RIEMANNIAN
MANIFOLDS 308 CONSTANT VECTOR FIELDS AND PARALLEL DISPLACEMENT 314 4.
ADDENDA TO THE THEORY OF DIFFERENTIATION ON A MANIFOLD 316 THE CURVATURE
TENSOR 316 THE RIEMANNIAN CONNECTION AND EXTERIOR DIFFERENTIAL FORMS 319
5. GEODESIC CURVES ON RIEMANNIAN MANIFOLDS 321 6. THE TANGENT BUNDLE AND
EXPONENTIAL MAPPING. NORMAL COORDINATES 326 7. SOME FURTHER PROPERTIES
OF GEODESIES 332 8. SYMMETRIC RIEMANNIAN MANIFOLDS 340 9. SOME EXAMPLES
346 VIII. CURVATURE 1. THE GEOMETRY OF SURFACES IN E 3 355 THE PRINCIPAL
CURVATURES AT A POINT OF A SURFACE 359 2. THE GAUSSIAN AND MEAN
CURVATURES OF A SURFACE 363 THE THEOREMA EGREGIUM OF GAUSS 366 3. BASIC
PROPERTIES OF THE RIEMANN CURVATURE TENSOR 371 4. CURVATURE FORMS AND
THE EQUATIONS OF STRUCTURE 378 5. DIFFERENTIATION OF COVARIANT TENSOR
FIELDS 384 6. MANIFOLDS OF CONSTANT CURVATURE 391 SPACES OF POSITIVE
CURVATURE 394 SPACES OF ZERO CURVATURE 396 SPACES OF CONSTANT NEGATIVE
CURVATURE 397 REFERENCES 403 INDEX 411 |
| any_adam_object | 1 |
| author | Boothby, William M. 1918- |
| author_GND | (DE-588)171984412 |
| author_facet | Boothby, William M. 1918- |
| author_role | aut |
| author_sort | Boothby, William M. 1918- |
| author_variant | w m b wm wmb |
| building | Verbundindex |
| bvnumber | BV016497055 |
| 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 350 SK 370 |
| classification_tum | MAT 537f MAT 582f |
| ctrlnum | (OCoLC)51536949 (DE-599)BVBBV016497055 |
| 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 |
| edition | revised second edition |
| format | Book |
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| id | DE-604.BV016497055 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T06:05:28Z |
| institution | BVB |
| isbn | 9780121160517 0121160513 |
| language | English |
| lccn | 2001097950 |
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| physical | xiv, 419 Seiten Illustrationen, Diagramme |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Academic Press |
| record_format | marc |
| spelling | Boothby, William M. 1918- (DE-588)171984412 aut An introduction to differentiable manifolds and Riemannian geometry William M. Boothby revised second edition Amsterdam ; London ; New York ; Oxford ; Paris ; Tokyo ; Boston ; San Diego ; San Francisco ; Singapore ; Sydney Academic Press [2003] © 2003 xiv, 419 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Literaturverzeichnis: Seite 403 - 409 Hier auch später erschienene, unveränderte Nachdrucke Geometria diferencial larpcal Geometria riemanniana larpcal Variedades diferenciáveis larpcal Differentiable manifolds Riemannian manifolds Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Riemannscher Raum (DE-588)4128295-4 gnd rswk-swf Differentiation Mathematik (DE-588)4149787-9 gnd rswk-swf Riemannsche Geometrie (DE-588)4128462-8 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 s DE-604 Riemannsche Geometrie (DE-588)4128462-8 s Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 s Riemannscher Raum (DE-588)4128295-4 s Differentiation Mathematik (DE-588)4149787-9 s HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010197036&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Boothby, William M. 1918- An introduction to differentiable manifolds and Riemannian geometry Geometria diferencial larpcal Geometria riemanniana larpcal Variedades diferenciáveis larpcal Differentiable manifolds Riemannian manifolds Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Riemannscher Raum (DE-588)4128295-4 gnd Differentiation Mathematik (DE-588)4149787-9 gnd Riemannsche Geometrie (DE-588)4128462-8 gnd |
| subject_GND | (DE-588)4012269-4 (DE-588)4037379-4 (DE-588)4128295-4 (DE-588)4149787-9 (DE-588)4128462-8 |
| title | An introduction to differentiable manifolds and Riemannian geometry |
| title_auth | An introduction to differentiable manifolds and Riemannian geometry |
| title_exact_search | An introduction to differentiable manifolds and Riemannian geometry |
| title_full | An introduction to differentiable manifolds and Riemannian geometry William M. Boothby |
| title_fullStr | An introduction to differentiable manifolds and Riemannian geometry William M. Boothby |
| title_full_unstemmed | An introduction to differentiable manifolds and Riemannian geometry William M. Boothby |
| title_short | An introduction to differentiable manifolds and Riemannian geometry |
| title_sort | an introduction to differentiable manifolds and riemannian geometry |
| topic | Geometria diferencial larpcal Geometria riemanniana larpcal Variedades diferenciáveis larpcal Differentiable manifolds Riemannian manifolds Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Riemannscher Raum (DE-588)4128295-4 gnd Differentiation Mathematik (DE-588)4149787-9 gnd Riemannsche Geometrie (DE-588)4128462-8 gnd |
| topic_facet | Geometria diferencial Geometria riemanniana Variedades diferenciáveis Differentiable manifolds Riemannian manifolds Differenzierbare Mannigfaltigkeit Mannigfaltigkeit Riemannscher Raum Differentiation Mathematik Riemannsche Geometrie |
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