Dirac operators in Riemannian geometry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
2000
|
| Series: | Graduate studies in mathematics
25 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 195 S. |
| ISBN: | 0821820559 9780821820551 |
Staff View
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Record in the Search Index
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| adam_text | DIRAC OPERATORS IN RIEMANNIAN GEOMETRY THOMAS FRIEDRICH TRANSLATED BY
ANDREAS NESTKE GRADUATE STUDIES IN MATHEMATICS VOLUME 25 AMERICAN
MATHEMATICAL SOCIETY PROVIDENCE, RHODE ISLAND CONTENTS INTRODUCTION XI
CHAPTER 1. CLIFFORD ALGEBRAS AND SPIN REPRESENTATION 1 1.1. LINEAR
ALGEBRA OF QUADRATIC FORMS 1 1.2. THE CLIFFORD ALGEBRA OF A QUADRATIC
FORM 4 1.3. CLIFFORD ALGEBRAS OF REAL NEGATIVE DEFINITE QUADRATIC FORMS
10 1.4. THE PIN AND THE SPIN GROUP 14 1.5. THE SPIN REPRESENTATION 20
1.6. THE GROUP SPIRF 25 1.7. REAL AND QUATERNIONIC STRUCTURES IN THE
SPACE OF N-SPINORS 29 1.8. REFERENCES AND EXERCISES 32 CHAPTER 2. SPIN
STRUCTURES 35 2.1. SPIN STRUCTURES ON S O(N)-PRINCIPAL BUNDLES 35 2.2.
SPIN STRUCTURES IN COVERING SPACES 42 2.3. SPIN STRUCTURES ON
G-PRINCIPAL BUNDLES 45 2.4. EXISTENCE OF SPIN C STRUCTURES 47 2.5.
ASSOCIATED SPINOR BUNDLES 53 2.6. REFERENCES AND EXERCISES 56 VN VIII
CONTENTS CHAPTER 3. DIRAC OPERATORS 57 3.1. CONNECTIONS IN SPINOR
BUNDLES 57 3.2. THE DIRAC AND THE LAPLACE OPERATOR IN THE SPINOR BUNDLE
67 3.3. THE SCHRODINGER-LICHNEROWICZ FORMULA 71 3.4. HERMITIAN MANIFOLDS
AND SPINORS 73 3.5. THE DIRAC OPERATOR OF A RIEMANNIAN SYMMETRIC SPACE
82 3.6. REFERENCES AND EXERCISES 88 CHAPTER 4. ANALYTICAL PROPERTIES OF
DIRAC OPERATORS 91 4.1. THE ESSENTIAL SELF-ADJOINTNESS OF THE DIRAC
OPERATOR IN I? 91 4.2. THE SPECTRUM OF DIRAC OPERATORS OVER COMPACT
MANIFOLDS 98 4.3. DIRAC OPERATORS ARE FREDHOLM OPERATORS 107 4.4.
REFERENCES AND EXERCISES 111 CHAPTER 5. EIGENVALUE ESTIMATES FOR THE
DIRAC OPERATOR AND TWISTOR SPINORS 113 5.1. LOWER ESTIMATES FOR THE
EIGENVALUES OF THE DIRAC OPERATOR 113 5.2. RIEMANNIAN MANIFOLDS WITH
KILLING SPINORS 116 5.3. THE TWISTOR EQUATION 121 5.4. UPPER ESTIMATES
FOR THE EIGENVALUES OF THE DIRAC OPERATOR 125 5.5. REFERENCES AND
EXERCISES 127 APPENDIX A. SEIBERG-WITTEN INVARIANTS 129 A.I. ON THE
TOPOLOGY OF 4-DIMENSIONAL MANIFOLDS 129 A.2. THE SEIBERG-WITTEN EQUATION
134 A.3. THE SEIBERG-WITTEN INVARIANT 138 A.4. VANISHING THEOREMS 144
A.5. THE CASE DIM 9^(3) = 0 146 A.6. THE KAHLER CASE 147 A.7. REFERENCES
153 APPENDIX B. PRINCIPAL BUNDLES AND CONNECTIONS 155 B.I. PRINCIPAL
FIBRE BUNDLES 155 CONTENTS IX B.2. THE CLASSIFICATION OF PRINCIPAL
BUNDLES 162 B.3. CONNECTIONS IN PRINCIPAL BUNDLES 163 B.4. ABSOLUTE
DIFFERENTIAL AND CURVATURE 166 B.5. CONNECTIONS IN J7(L)-PRINCIPAL
BUNDLES AND THE WEYL THEOREM 169 B.6. REDUCTIONS OF CONNECTIONS 173 B.7.
PROBENIUS THEOREM 174 B.8. THE FREUDENTHAL-YAMABE THEOREM 177 B.9.
HOLONOMY THEORY 177 B.10. REFERENCES 178 BIBLIOGRAPHY 179 INDEX 193
|
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| ctrlnum | (OCoLC)247647093 (DE-599)BVBBV013265702 |
| dewey-full | 516.3/73 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/73 |
| dewey-search | 516.3/73 |
| dewey-sort | 3516.3 273 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T18:42:46Z |
| institution | BVB |
| isbn | 0821820559 9780821820551 |
| language | English |
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| physical | XVI, 195 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spelling | Friedrich, Thomas 1949-2018 Verfasser (DE-588)14097413X aut Dirac-Operatoren in der Riemannschen Geometrie Dirac operators in Riemannian geometry Thomas Friedrich Providence, RI American Math. Soc. 2000 XVI, 195 S. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 25 Riemannsche Geometrie - Dirac-Operator Dirac-Operator (DE-588)4150118-4 gnd rswk-swf Riemannsche Geometrie (DE-588)4128462-8 gnd rswk-swf Riemannsche Geometrie (DE-588)4128462-8 s Dirac-Operator (DE-588)4150118-4 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-2080-2 Graduate studies in mathematics 25 (DE-604)BV009739289 25 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009043592&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Friedrich, Thomas 1949-2018 Dirac operators in Riemannian geometry Graduate studies in mathematics Riemannsche Geometrie - Dirac-Operator Dirac-Operator (DE-588)4150118-4 gnd Riemannsche Geometrie (DE-588)4128462-8 gnd |
| subject_GND | (DE-588)4150118-4 (DE-588)4128462-8 |
| title | Dirac operators in Riemannian geometry |
| title_alt | Dirac-Operatoren in der Riemannschen Geometrie |
| title_auth | Dirac operators in Riemannian geometry |
| title_exact_search | Dirac operators in Riemannian geometry |
| title_full | Dirac operators in Riemannian geometry Thomas Friedrich |
| title_fullStr | Dirac operators in Riemannian geometry Thomas Friedrich |
| title_full_unstemmed | Dirac operators in Riemannian geometry Thomas Friedrich |
| title_short | Dirac operators in Riemannian geometry |
| title_sort | dirac operators in riemannian geometry |
| topic | Riemannsche Geometrie - Dirac-Operator Dirac-Operator (DE-588)4150118-4 gnd Riemannsche Geometrie (DE-588)4128462-8 gnd |
| topic_facet | Riemannsche Geometrie - Dirac-Operator Dirac-Operator Riemannsche Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009043592&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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