Complex differential geometry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
[Providence, RI]
AMS [u.a.]
2001
|
| Edition: | Reprint. with corr. |
| Series: | AMS/IP studies in advanced mathematics
18 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 264 S. |
| ISBN: | 0821829602 |
Staff View
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Record in the Search Index
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| adam_text | AMS/IP STUDIES IN ADVANCED MATHEMATICS VOLUME 18 COMPLEX DIFFERENTIAL
GEOMETRY FANGYANG ZHENG AMERICAN MATHEMATICAL SOCIETY * INTERNATIONAL
PRESS --W P CONTENTS PREFACE XI PART 1. RIEMANNIAN GEOMETRY 1 CHAPTER 1.
DIFFERENTIABLE MANIFOLDS AND VECTOR BUNDLES 3 1.1. DIFFERENTIABLE
MANIFOLDS 3 1.2. TANGENT SPACES AND VECTOR FIELDS 5 1.3. VECTOR BUNDLES
8 1.4. TANGENT BUNDLES AND TENSOR FIELDS 11 1.5. THE TOPOLOGY OF SMOOTH
MANIFOLDS 14 1.6. LIE GROUPS AND LIE ALGEBRAS 16 APPENDIX: TOPOLOGY,
HOMOTOPY AND COVERING SPACES 20 EXERCISES 23 CHAPTER 2. METRIC,
CONNECTION, AND CURVATURE 29 2.1. METRIC, CONNECTION, AND CURVATURE 29
2.2. LINEAR CONNECTIONS AND GEODESIES 31 2.3. RIEMANNIAN METRICS AND
RIEMANNIAN CONNECTIONS 34 2.4. SECTIONAL, RICCI AND SCALAR CURVATURES 37
2.5. CARTAN S STRUCTURE EQUATIONS AND EXAMPLES 40 EXERCISES 45 CHAPTER
3. THE GEOMETRY OF COMPLETE RIEMANNIAN MANIFOLDS 49 3.1. RIEMANNIAN
DISTANCE 49 3.2. COMPLETENESS AND HOPF-RINOW THEOREM 53 3.3. JACOBI
FIELDS AND CONJUGATE POINTS 56 3.4. CARTAN-AMBROSE-HICKS THEOREM AND
SPACE FORMS 64 3.5. HOMOGENEOUS AND SYMMETRIC SPACES 66 3.6. HODGE
THEOREM AND COMPARISON THEOREMS 70 EXERCISES 74 PART 2. COMPLEX
MANIFOLDS 81 CHAPTER 4. COMPLEX MANIFOLDS AND ANALYTIC VARIETIES 83 4.1.
HOLOMORPHIC FUNCTIONS OF ONE OR MORE COMPLEX VARIABLES 83 4.2.
DEFINITION AND EXAMPLES OF COMPLEX MANIFOLDS 86 4.3. THE ALMOST COMPLEX
STRUCTURE 89 4.4. MORE EXAMPLES 92 4.5. HYPERSURFACES AND ANALYTIC
SUBVARIETIES 95 4.6. DIVISORS AND ANALYTIC CYCLES 99 X CONTENTS
EXERCISES 101 CHAPTER 5. HOLOMORPHIC VECTOR BUNDLES, SHEAVES AND
COHOMOLOGY 105 5.1. HOLOMORPHIC VECTOR BUNDLES 105 5.2. SHEAVES 108 5.3.
SHEAF COHOMOLOGY GROUPS 112 5.4. HOLOMORPHIC LINE BUNDLES 115 5.5. CHERN
CLASSES 119 EXERCISES 123 CHAPTER 6. COMPACT COMPLEX SURFACES 127 6.1.
THE TOPOLOGICAL INVARIANTS 127 6.2. THE KODAIRA DIMENSION AND THE
ALGEBRAIC DIMENSION 132 6.3. EXAMPLES OF SURFACES 137 6.4.
ENRIQUES-KODAIRA CLASSIFICATION THEORY FOR SURFACES 142 EXERCISES 151
PART 3. KAHLER GEOMETRY 155 CHAPTER 7. HERMITIAN AND KAHLER METRICS 157
7.1. CONNECTIONS ON VECTOR BUNDLES AND THEIR CURVATURE 157 7.2. CHERN
FORMS OF A COMPLEX VECTOR BUNDLE 160 7.3. HERMITIAN BUNDLES 166 7.4.
HERMITIAN AND KAHLER METRICS ON COMPLEX MANIFOLDS 170 7.5. THE CURVATURE
OF A HERMITIAN OR KAHLER METRIC 176 7.6. WU S THEOREM, SCHWARZ LEMMA AND
HARTOGS PHENOMENON 181 EXERCISES 187 CHAPTER 8. COMPACT KAHLER MANIFOLDS
191 8.1. HODGE THEOREM AND HODGE DECOMPOSITION 191 8.2. THE HARD
LEFSCHETZ THEOREM 195 8.3. KODAIRA VANISHING AND EMBEDDING THEOREMS 200
8.4. AMPLE SUBVARIETIES AND AMPLE VECTOR BUNDLES 204 8.5. HERMITIAN
SYMMETRIC SPACES AND KAHLER C-SPACES 208 8.6. THE HARTSHORNE-FRANKEL
CONJECTURE 213 EXERCISES 219 CHAPTER 9. KAHLER GEOMETRY 221 9.1.
CALABI S CONJECTURE AND KAHLER-EINSTEIN METRICS 221 9.2. COROLLARIES OF
YAU S THEOREMS 225 9.3. INVARIANT METRICS 230 9.4. HARMONIC MAPS AND THE
RIGIDITY THEOREMS 236 9.5. NON-POSITIVELY CURVED KAHLER SURFACES 242
EXERCISES 249 BIBLIOGRAPHY 255 INDEX 259
|
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| discipline | Mathematik |
| edition | Reprint. with corr. |
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| indexdate | 2024-07-09T20:03:35Z |
| institution | BVB |
| isbn | 0821829602 |
| language | English |
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| physical | VIII, 264 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | AMS [u.a.] |
| record_format | marc |
| series | AMS/IP studies in advanced mathematics |
| series2 | AMS/IP studies in advanced mathematics |
| spelling | Zheng, Fangyang Verfasser aut Complex differential geometry Fangyang Zheng Reprint. with corr. [Providence, RI] AMS [u.a.] 2001 VIII, 264 S. txt rdacontent n rdamedia nc rdacarrier AMS/IP studies in advanced mathematics 18 Complex manifolds Geometry, Differential Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd rswk-swf Komplexe Mannigfaltigkeit (DE-588)4031996-9 s Differentialgeometrie (DE-588)4012248-7 s DE-604 AMS/IP studies in advanced mathematics 18 (DE-604)BV011103148 18 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013005653&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zheng, Fangyang Complex differential geometry AMS/IP studies in advanced mathematics Complex manifolds Geometry, Differential Differentialgeometrie (DE-588)4012248-7 gnd Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4031996-9 |
| title | Complex differential geometry |
| title_auth | Complex differential geometry |
| title_exact_search | Complex differential geometry |
| title_full | Complex differential geometry Fangyang Zheng |
| title_fullStr | Complex differential geometry Fangyang Zheng |
| title_full_unstemmed | Complex differential geometry Fangyang Zheng |
| title_short | Complex differential geometry |
| title_sort | complex differential geometry |
| topic | Complex manifolds Geometry, Differential Differentialgeometrie (DE-588)4012248-7 gnd Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd |
| topic_facet | Complex manifolds Geometry, Differential Differentialgeometrie Komplexe Mannigfaltigkeit |
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| volume_link | (DE-604)BV011103148 |
| work_keys_str_mv | AT zhengfangyang complexdifferentialgeometry |