Lectures on Kähler manifolds:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Zürich
European Mathematical Society
2006
|
| Schriftenreihe: | Lectures in mathematics and physics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. [165] - 170 |
| Beschreibung: | X, 172 S. |
| ISBN: | 9783037190258 3037190256 |
Internformat
MARC
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| 100 | 1 | |a Ballmann, Werner |d 1951- |e Verfasser |0 (DE-588)143941178 |4 aut | |
| 245 | 1 | 0 | |a Lectures on Kähler manifolds |c Werner Ballmann |
| 264 | 1 | |a Zürich |b European Mathematical Society |c 2006 | |
| 300 | |a X, 172 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Lectures in mathematics and physics | |
| 500 | |a Literaturverz. S. [165] - 170 | ||
| 650 | 4 | |a Variétés kählériennes | |
| 650 | 4 | |a Kählerian manifolds | |
| 650 | 0 | 7 | |a Kähler-Mannigfaltigkeit |0 (DE-588)4162978-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Kähler-Mannigfaltigkeit |0 (DE-588)4162978-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |a Ballmann, Werner, 1951- |t Lectures on Kähler manifolds |z 978-3-03719-525-3 |w (DE-604)BV036747104 |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-015677183 | ||
Datensatz im Suchindex
| _version_ | 1804136556352503808 |
|---|---|
| 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
|
| adam_txt |
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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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T17:44:03Z |
| indexdate | 2024-07-09T20:58:17Z |
| institution | BVB |
| isbn | 9783037190258 3037190256 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015677183 |
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| publishDate | 2006 |
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| spelling | Ballmann, Werner 1951- Verfasser (DE-588)143941178 aut Lectures on Kähler manifolds Werner Ballmann Zürich European Mathematical Society 2006 X, 172 S. txt rdacontent n rdamedia nc rdacarrier Lectures in mathematics and physics Literaturverz. S. [165] - 170 Variétés kählériennes Kählerian manifolds Kähler-Mannigfaltigkeit (DE-588)4162978-4 gnd rswk-swf Kähler-Mannigfaltigkeit (DE-588)4162978-4 s DE-604 Erscheint auch als Ballmann, Werner, 1951- Lectures on Kähler manifolds 978-3-03719-525-3 (DE-604)BV036747104 Digitalisierung UB Regensburg application/pdf 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 Inhaltsverzeichnis |
| 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_exact_search_txtP | 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 |
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