Verfügbarkeit: Global calculus

Global calculus:

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Bibliographische Detailangaben
1. Verfasser:	Ramanan, Sundararaman 1937- (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Providence, R.I. American Mathematical Society 2005
Schriftenreihe:	Graduate studies in mathematics 65
Schlagworte:	Espaces analytiques Fibrados vetoriais (geometria diferencial) Géométrie algébrique Géométrie différentielle Opérateurs différentiels aGeometry, Algebraic aDifferential operators aAnalytic spaces aDifferential geometry Analytischer Raum Differentialgeometrie Algebraische Geometrie Differentialoperator
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	XI, 316 S.
ISBN:	9780821837023 0821837028

Internformat

MARC


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Datensatz im Suchindex

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adam_text	Contents Preface ix Chapter 1. Sheaves and Differential Manifolds: Definitions and Examples 1 1. Sheaves and Presheaves 2 2. Basic Constructions 9 3. Differential Manifolds 12 4. Lie Groups; Action on a Manifold 23 Exercises 25 Chapter 2. Differential Operators 27 1. First Order Differential Operators 27 2. Locally Free Sheaves and Vector Bundles 29 3. Flow of a Vector Field 38 4. Theorem of Frobenius 46 5. Tensor Fields; Lie Derivative 50 6. The Exterior Derivative; de Rham Complex 54 7. Differential Operators of Higher Order 61 Exercises 70 Chapter 3. Integration on Differential Manifolds 73 1. Integration on a Manifold 73 2. Sheaf of Densities 79 3. Adjoints of Differential Operators 85 v vi Contents Exercises 90 Chapter 4. Cohomology of Sheaves and Applications 93 1. Injective Sheaves 93 2. Sheaf Cohomology 98 3. Cohomology through Other Resolutions 105 4. Singular and Sheaf Cohomologies 107 5. Cech and Sheaf Cohomologies 114 6. Differentiable Simplices; de Rham s Theorem 117 Exercises 122 Chapter 5. Connections on Principal and Vector Bundles; Lifting of Symbols 125 1. Connections in a Vector Bundle 125 2. The Space of All Connections on a Bundle 131 3. Principal Bundles 135 4. Connections on Principal Bundles 143 5. Curvature 148 6. Chern Weil Theory 154 7. Holonomy Group; Ambrose Singer Theorem 164 Exercises 168 Chapter 6. Linear Connections 171 1. Linear Connections 171 2. Lifting of Symbols and Torsion 177 Exercises 182 Chapter 7. Manifolds with Additional Structures 185 1. Reduction of the Structure Group 185 2. Torsion Free G Connections 194 3. Complex Manifolds 197 4. The Outer Gauge Group 201 5. Riemannian Geometry 207 6. Riemannian Curvature Tensor 211 7. Ricci, Scalar and Weyl Curvature Tensors 219 8. Clifford Structures and the Dirac Operator 224 Chapter 8. Local Analysis of Elliptic Operators 229 1. Regularisation 229 Contents vii 2. A Characterisation of Densities 232 3. Schwartz Space of Functions and Densities 233 4. Fourier Transforms 238 5. Distributions 242 6. Theorem of Sobolev 245 7. Interior Regularity of Elliptic Solutions 251 Chapter 9. Vanishing Theorems and Applications 257 1. Elliptic Operators on Differential Manifolds 257 2. Elliptic Complexes 261 3. Composition Formula 270 4. A Vanishing Theorem 276 5. Hodge Decomposition 279 6. Lefschetz Decomposition 281 7. Kodaira s Vanishing Theorem 287 8. The Imbedding Theorem 292 Appendix 301 1. Algebra 301 2. Topology 305 3. Analysis 307 Bibliography 311 Index 313
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spelling	Ramanan, Sundararaman 1937- Verfasser (DE-588)115463313 aut Global calculus S. Ramanan Providence, R.I. American Mathematical Society 2005 XI, 316 S. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 65 Espaces analytiques Fibrados vetoriais (geometria diferencial) larpcal Géométrie algébrique Géométrie différentielle Opérateurs différentiels aGeometry, Algebraic aDifferential operators aAnalytic spaces aDifferential geometry Analytischer Raum (DE-588)4001871-4 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Differentialoperator (DE-588)4012251-7 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 s Differentialoperator (DE-588)4012251-7 s Analytischer Raum (DE-588)4001871-4 s Differentialgeometrie (DE-588)4012248-7 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-2107-6 Graduate studies in mathematics 65 (DE-604)BV009739289 65 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013180980&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Ramanan, Sundararaman 1937- Global calculus Graduate studies in mathematics Espaces analytiques Fibrados vetoriais (geometria diferencial) larpcal Géométrie algébrique Géométrie différentielle Opérateurs différentiels aGeometry, Algebraic aDifferential operators aAnalytic spaces aDifferential geometry Analytischer Raum (DE-588)4001871-4 gnd Differentialgeometrie (DE-588)4012248-7 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Differentialoperator (DE-588)4012251-7 gnd
subject_GND	(DE-588)4001871-4 (DE-588)4012248-7 (DE-588)4001161-6 (DE-588)4012251-7
title	Global calculus
title_auth	Global calculus
title_exact_search	Global calculus
title_full	Global calculus S. Ramanan
title_fullStr	Global calculus S. Ramanan
title_full_unstemmed	Global calculus S. Ramanan
title_short	Global calculus
title_sort	global calculus
topic	Espaces analytiques Fibrados vetoriais (geometria diferencial) larpcal Géométrie algébrique Géométrie différentielle Opérateurs différentiels aGeometry, Algebraic aDifferential operators aAnalytic spaces aDifferential geometry Analytischer Raum (DE-588)4001871-4 gnd Differentialgeometrie (DE-588)4012248-7 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Differentialoperator (DE-588)4012251-7 gnd
topic_facet	Espaces analytiques Fibrados vetoriais (geometria diferencial) Géométrie algébrique Géométrie différentielle Opérateurs différentiels aGeometry, Algebraic aDifferential operators aAnalytic spaces aDifferential geometry Analytischer Raum Differentialgeometrie Algebraische Geometrie Differentialoperator
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013180980&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV009739289
work_keys_str_mv	AT ramanansundararaman globalcalculus

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