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Lectures on Kähler manifolds:

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Bibliographische Detailangaben
Beteilige Person:	Ballmann, Werner 1951- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Zürich European Mathematical Society 2006
Schriftenreihe:	Lectures in mathematics and physics
Schlagwörter:	Variétés kählériennes Kählerian manifolds Kähler-Mannigfaltigkeit
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015677183&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Beschreibung:	Literaturverz. S. [165] - 170
Umfang:	X, 172 S.
ISBN:	9783037190258 3037190256

Internformat

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Datensatz im Suchindex

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adam_text	Contents 1 Preliminaries ................................ 1 1.1 Differential Forms .......................... 2 1.2 Exterior Derivative .......................... 4 1.3 Laplace Operator ........................... 6 1.4 Hodge Operator ........................... 8 2 Complex Manifolds ............................ 11 2.1 Complex Vector Fields ........................ 18 2.2 Differential Forms .......................... 20 2.3 Compatible Metrics ......................... 23 2.4 Blowing Up Points .......................... 24 3 Holomorphic Vector Bundles ....................... 29 3.1 Dolbeault Cohomology ....................... 29 3.2 Chern Connection .......................... 31 3.3 Some Formulas ........................... 34 3.4 Holomorphic Line Bundles ..................... 36 4 Kahler Manifolds ............................. 41 4.1 Kahler Form and Volume ...................... 48 4.2 Levi-Civita Connection ....................... 50 4.3 Curvature Tensor ........................... 52 4.4 Ricci Tensor ............................. 54 4.5 Holonomy .............................. 55 4.6 KillingFields ............................ 57 5 Cohomology of Kahler Manifolds ..................... 60 5.1 Lefschetz Map and Differentials ................... 62 5.2 Lef schetz Map and Cohomology .................. 65 5.3 The ddc-Lemma and Formality ................... 71 5.4 Some Vanishing Theorems ...................... 75 6 Ricci Curvature and Global Structure ................... 80 6.1 Ricci-Fiat Kahler Manifolds ..................... 81 6.2 Nonnegative Ricci Curvature .................... 82 6.3 Ricci Curvature and Laplace Operator ................ 83 7 Calabi Conjecture ............................. 86 7.1 Uniqueness .............................. 89 7.2 Regularity .............................. 91 7.3 Existence ............................... 92 7.4 Obstructions ............................. 97 Contents 8 Kahler Hyperbolic Spaces......................... 103 8.1 Kahler Hyperbolicity and Spectram................. 106 8.2 Non- Vanishing of Cohomology ................... ПО 9 Kodaira Embedding Theorem....................... 114 9.1 Proof of the Embedding Theorem.................. 116 9.2 Two Applications .......................... 120 Appendix A Chern-Weil Theory ....................... 121 A.1 Chern Classes and Character .................... 127 A.2 Euler Class .............................. 131 Appendix В Symmetric Spaces ........................ 134 B.I Symmetric Pairs ........................... 138 B.2 Examples ............................... 144 B.3 Hermitian Symmetric Spaces .................... 152 Appendix С Remarks on Differential Operators ............... 157 C.I Dirac Operators ........................... 160 C.2 L2-de Rham Cohomology ...................... 162 C.3 L2-Dolbeault Cohomology ..................... 163 Literature ................................... 165 Index ..................................... 171
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isbn	9783037190258 3037190256
language	English
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physical	X, 172 S.
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series2	Lectures in mathematics and physics
spellingShingle	Ballmann, Werner 1951- Lectures on Kähler manifolds Variétés kählériennes Kählerian manifolds Kähler-Mannigfaltigkeit (DE-588)4162978-4 gnd
subject_GND	(DE-588)4162978-4
title	Lectures on Kähler manifolds
title_auth	Lectures on Kähler manifolds
title_exact_search	Lectures on Kähler manifolds
title_full	Lectures on Kähler manifolds Werner Ballmann
title_fullStr	Lectures on Kähler manifolds Werner Ballmann
title_full_unstemmed	Lectures on Kähler manifolds Werner Ballmann
title_short	Lectures on Kähler manifolds
title_sort	lectures on kahler manifolds
topic	Variétés kählériennes Kählerian manifolds Kähler-Mannigfaltigkeit (DE-588)4162978-4 gnd
topic_facet	Variétés kählériennes Kählerian manifolds Kähler-Mannigfaltigkeit
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015677183&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT ballmannwerner lecturesonkahlermanifolds

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