Differential geometry of manifolds:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Alpha Science Internat.
2007
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 298 S. Ill., graph. Darst. |
| ISBN: | 9781842653715 |
Staff View
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| 245 | 1 | 0 | |a Differential geometry of manifolds |c U. C. De ; A. A. Shaikh |
| 264 | 1 | |a Oxford |b Alpha Science Internat. |c 2007 | |
| 300 | |a XI, 298 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 4 | |a Differentiable manifolds | |
| 650 | 4 | |a Differentiable manifolds | |
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Record in the Search Index
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| adam_text | DIFFERENTIAL GEOMETRY OF MANIFOLDS U.C. DE A.A. SHAIKH ALPHA SCIENCE
INTERNATIONAL LTD. OXFORD, U.K. CONTENTS PREFACE VII I SOME
PRELIMINARIES 1 1.0 INTRODUCTION 1 1.1 METRIC SPACES , 1 1.2 TOPOLOGICAL
SPACES 3 1.3 METRIC TOPOLOGIES AND METRIZABLE SPACES 3 1.4 BASE FOR THE
NEIGHBOURHOOD SYSTEM OF A POINT AND BASE FOR A TOPOLOGY 5 1.5 CONTINUITY
IN TOPOLOGICAL SPACES 6 1.6 CONNECTEDNESS AND COMPACTNESS 7 1.7
COUNTABILITY AND SEPARATION AXIOMS ; 10 1.8 LINEAR ALGEBRA 15 II
DIFFERENTIABLE MANIFOLDS 27 HI INTRODUCTION 27 II.2 DIFFERENTIABLE
STRUCTURES DEFINED ON SETS 44 H.3 DIFFERENTIABLE FUNCTIONS ON A MANIFOLD
50 II.4 TANGENT SPACES 54 N.4.1 TANGENT VECTOR AS AN EQUIVALENCE CLASS
OF CURVES 55 N.4.2 TANGENT VECTOR AS A DIRECTIONAL DERIVATIVE OPERATOR
56 N.4.3 ALGEBRAIC APPROACH OF TANGENT VECTORS 63 N.4.4 DIFFERENTIALS OF
SMOOTH MAPS 70 N.5 VECTOR FIELDS ON DIFFERENTIABLE MANIFOLDS 92 N.5.1
VECTOR FIELDS AND LIE BRACKET 92 N.5.2 /-RELATED VECTOR FIELDS 107 II.6
INTEGRAL CURVES AND FLOWS 110 11.6.1 INTEGRAL CURVES 110 11.6.2 ONE
PARAMETER GROUP OFTRANSFORMATIONS OF A MANIFOLD 118 III EXTERIOR ALGEBRA
AND EXTERIOR DERIVATIVE 131 M.L TENSOR PRODUCTS.... 131 M.2
TENSORALGEBRA 134 IH.3 EXTERIOR ALGEBRA 138 M.4 EXTERIOR DERIVATIVE 150
IV LIE GROUP AND LIE ALGEBRAS 161 IV! INTRODUCTION 161 X CONTENTS IV2
THE LIE ALGEBRA OFA LIE GROUP 166 IV3 LIE GROUPS HOMOMORPHISM AND
ISOMORPHISM 171 IV.4 ONE PARAMETER SUBGROUPS AND EXPONENTIAL MAP 173
IV.5 LIE TRANSFORMATION GROUPS 176 IV6 LIE DERIVATIVE 181 V FIBRE
BUNDLES 188 VI PRINCIPAL FIBRE BUNDLE 188 V2 DEFINITION OF CROSS SECTION
189 V3 LINEAR FRAME BUNDLE :.... 190 V.4 ASSOCIATED PRINCIPAL BUNDLE 190
V5 VECTORBUNDLES :.... 191 V.6 BUNDLE HOMOMORPHISM 192 V7 TANGENTBUNDLE
... 192 V8 FUNDAMENTAL VECTOR FIELD ......:..... 193 VI LINEAR
CONNECTIONS 194 VII AFFINE CONNECTIONS 194 VL2 TORSION TENSOR OF AN
AFFINE CONNECTION . 203 VI3 CURVATURE TENSOR OF AN AFFINE CONNECTION
210 VL4 SOME EXERCISES 214 VII RIEMANNIAN MANIFOLDS 217 VII.1
INTRODUCTION 217 VB.2 RIEMANNIAN CONNECTION.... :.... 222 VII.3 RIEMANN
CURVATURE TENSOR 228 W.4 RIEMANNIAN MANIFOLD AS A METIRC SPACE 239 VII.5
SOME CONNECTIONS ON A RIEMANNIAN MANIFOLD.... 243 VII.6 SECTIONAL
CURVATURE OF A RIEMANNIAN MANIFOLD : 252 VII.7 SOME TRANSFORMATIONS ON
RIEMANNIAN MANIFOLDS 259 VIII SUBMANIFOLDS 274 VIN.L SUBMANIFOLDS OFA
RIEMANNIAN MANIFOLD :. 274 VHI.2 INDUCED CONNECTION AND SECOND
FUNDAMENTAL FORM 276 VHI.3 EQUATIONS OF GAUSS, CODAZZI AND RICCI ;....
277 VFFL.4 MEAN CURVATURE 278 IX COMPLEX MANIFOLDS 279 EX.1 ALGEBRAIC
PRELIMINARIES ;..: 279 IX.2 ALMOST HERMITE MANIFOLD 282 K.3 KAHLER
MANIFOLD 283 K.4 ALMOST TACHIBANA MANIFOLD 285 CONTENTS XI IX.5
HOLOMORPHIC SECTIONAL CURVATURE 286 DC.6 F-CONNECTION 288 EX.7
HOLOMORPHICALLY PLANAR CURVES 292 BIBLIOGRAPHY 293 INDEX 294
|
| adam_txt |
DIFFERENTIAL GEOMETRY OF MANIFOLDS U.C. DE A.A. SHAIKH ALPHA SCIENCE
INTERNATIONAL LTD. OXFORD, U.K. CONTENTS PREFACE VII I SOME
PRELIMINARIES 1 1.0 INTRODUCTION 1 1.1 METRIC SPACES , 1 1.2 TOPOLOGICAL
SPACES 3 1.3 METRIC TOPOLOGIES AND METRIZABLE SPACES 3 1.4 BASE FOR THE
NEIGHBOURHOOD SYSTEM OF A POINT AND BASE FOR A TOPOLOGY 5 1.5 CONTINUITY
IN TOPOLOGICAL SPACES 6 1.6 CONNECTEDNESS AND COMPACTNESS 7 1.7
COUNTABILITY AND SEPARATION AXIOMS ; 10 1.8 LINEAR ALGEBRA 15 II
DIFFERENTIABLE MANIFOLDS 27 HI INTRODUCTION 27 II.2 DIFFERENTIABLE
STRUCTURES DEFINED ON SETS 44 H.3 DIFFERENTIABLE FUNCTIONS ON A MANIFOLD
50 II.4 TANGENT SPACES 54 N.4.1 TANGENT VECTOR AS AN EQUIVALENCE CLASS
OF CURVES 55 N.4.2 TANGENT VECTOR AS A DIRECTIONAL DERIVATIVE OPERATOR
56 N.4.3 ALGEBRAIC APPROACH OF TANGENT VECTORS 63 N.4.4 DIFFERENTIALS OF
SMOOTH MAPS 70 N.5 VECTOR FIELDS ON DIFFERENTIABLE MANIFOLDS 92 N.5.1
VECTOR FIELDS AND LIE BRACKET 92 N.5.2 /-RELATED VECTOR FIELDS 107 II.6
INTEGRAL CURVES AND FLOWS 110 11.6.1 INTEGRAL CURVES 110 11.6.2 ONE
PARAMETER GROUP OFTRANSFORMATIONS OF A MANIFOLD 118 III EXTERIOR ALGEBRA
AND EXTERIOR DERIVATIVE 131 M.L TENSOR PRODUCTS. 131 M.2
TENSORALGEBRA 134 IH.3 EXTERIOR ALGEBRA 138 M.4 EXTERIOR DERIVATIVE 150
IV LIE GROUP AND LIE ALGEBRAS 161 IV! INTRODUCTION 161 X CONTENTS IV2
THE LIE ALGEBRA OFA LIE GROUP 166 IV3 LIE GROUPS HOMOMORPHISM AND
ISOMORPHISM 171 IV.4 ONE PARAMETER SUBGROUPS AND EXPONENTIAL MAP 173
IV.5 LIE TRANSFORMATION GROUPS 176 IV6 LIE DERIVATIVE 181 V FIBRE
BUNDLES 188 VI PRINCIPAL FIBRE BUNDLE 188 V2 DEFINITION OF CROSS SECTION
189 V3 LINEAR FRAME BUNDLE :. 190 V.4 ASSOCIATED PRINCIPAL BUNDLE 190
V5 VECTORBUNDLES :. 191 V.6 BUNDLE HOMOMORPHISM 192 V7 TANGENTBUNDLE
'. 192 V8 FUNDAMENTAL VECTOR FIELD .:. 193 VI LINEAR
CONNECTIONS 194 VII AFFINE CONNECTIONS 194 VL2 TORSION TENSOR OF AN
AFFINE CONNECTION '. 203 VI3 CURVATURE TENSOR OF AN AFFINE CONNECTION
210 VL4 SOME EXERCISES 214 VII RIEMANNIAN MANIFOLDS 217 VII.1
INTRODUCTION 217 VB.2 RIEMANNIAN CONNECTION. :. 222 VII.3 RIEMANN
CURVATURE TENSOR 228 W.4 RIEMANNIAN MANIFOLD AS A METIRC SPACE 239 VII.5
SOME CONNECTIONS ON A RIEMANNIAN MANIFOLD. 243 VII.6 SECTIONAL
CURVATURE OF A RIEMANNIAN MANIFOLD : 252 VII.7 SOME TRANSFORMATIONS ON
RIEMANNIAN MANIFOLDS 259 VIII SUBMANIFOLDS 274 VIN.L SUBMANIFOLDS OFA
RIEMANNIAN MANIFOLD :. 274 VHI.2 INDUCED CONNECTION AND SECOND
FUNDAMENTAL FORM 276 VHI.3 EQUATIONS OF GAUSS, CODAZZI AND RICCI ;.
277 VFFL.4 MEAN CURVATURE 278 IX COMPLEX MANIFOLDS 279 EX.1 ALGEBRAIC
PRELIMINARIES ;.: 279 IX.2 ALMOST HERMITE MANIFOLD 282 K.3 KAHLER
MANIFOLD 283 K.4 ALMOST TACHIBANA MANIFOLD 285 CONTENTS XI IX.5
HOLOMORPHIC SECTIONAL CURVATURE 286 DC.6 F-CONNECTION 288 EX.7
HOLOMORPHICALLY PLANAR CURVES 292 BIBLIOGRAPHY 293 INDEX 294 |
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| author | De, Uday Chand |
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| ctrlnum | (OCoLC)145338463 (DE-599)BVBBV035115549 |
| dewey-full | 516.07 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.07 |
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| dewey-sort | 3516.07 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| index_date | 2024-07-02T22:19:26Z |
| indexdate | 2024-07-09T21:22:40Z |
| institution | BVB |
| isbn | 9781842653715 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016783302 |
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| physical | XI, 298 S. Ill., graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
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| publisher | Alpha Science Internat. |
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| spelling | De, Uday Chand Verfasser (DE-588)136704794 aut Differential geometry of manifolds U. C. De ; A. A. Shaikh Oxford Alpha Science Internat. 2007 XI, 298 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Differentiable manifolds Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd rswk-swf Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 s DE-604 Shaikh, Absos Ali Sonstige (DE-588)136704840 oth GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016783302&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | De, Uday Chand Differential geometry of manifolds Differentiable manifolds Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd |
| subject_GND | (DE-588)4012269-4 |
| title | Differential geometry of manifolds |
| title_auth | Differential geometry of manifolds |
| title_exact_search | Differential geometry of manifolds |
| title_exact_search_txtP | Differential geometry of manifolds |
| title_full | Differential geometry of manifolds U. C. De ; A. A. Shaikh |
| title_fullStr | Differential geometry of manifolds U. C. De ; A. A. Shaikh |
| title_full_unstemmed | Differential geometry of manifolds U. C. De ; A. A. Shaikh |
| title_short | Differential geometry of manifolds |
| title_sort | differential geometry of manifolds |
| topic | Differentiable manifolds Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd |
| topic_facet | Differentiable manifolds Differenzierbare Mannigfaltigkeit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016783302&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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