Sasakian geometry:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Oxford University Press
2008
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Oxford mathematical monographs
Oxford Science Publications |
| Schlagworte: | |
| Online-Zugang: | Table of contents only Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XI, 613 S. |
| ISBN: | 9780198564959 |
Internformat
MARC
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| 035 | |a (OCoLC)140107626 | ||
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| 100 | 1 | |a Boyer, Charles P. |d 1942- |e Verfasser |0 (DE-588)137447094 |4 aut | |
| 245 | 1 | 0 | |a Sasakian geometry |c Charles P. Boyer and Krzysztof Galicki |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Oxford |b Oxford University Press |c 2008 | |
| 300 | |a XI, 613 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Oxford mathematical monographs | |
| 490 | 0 | |a Oxford Science Publications | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Sasakian manifolds | |
| 650 | 4 | |a Geometry | |
| 650 | 0 | 7 | |a Mannigfaltigkeit |0 (DE-588)4037379-4 |2 gnd |9 rswk-swf |
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| 689 | 1 | |8 1\p |5 DE-604 | |
| 700 | 1 | |a Galicki, Krzysztof |d 1958-2007 |e Verfasser |0 (DE-588)137447116 |4 aut | |
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| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804137236600455168 |
|---|---|
| adam_text | Contents
Preface
v
Introduction
1
Chapter
1.
Structures on Manifolds
9
1.1.
Sheaves and Sheaf Cohomology
9
1.2.
Principal and Associated Bundles
14
1.3.
Connections in Principal and Associated Vector Bundles
18
1.4.
G-Structures
23
1.5.
Pseudogroup Structures
36
1.6.
Group Actions on Manifolds
38
Chapter
2.
Foliations
51
2.1.
Examples of Foliations
51
2.2.
Haefliger Structures
52
2.3.
Leaf Holonomy and the Holonomy Groupoid
54
2.4.
Basic Cohomology
59
2.5.
Transverse Geometry
60
2.6.
Riemannian Flows
69
Chapter
3. Kahler
Manifolds
75
3.1.
Complex Manifolds and
Kahler
Metrics
76
3.2.
Curvature of
Kahler
Manifolds
82
3.3.
Hodge Theory on
Kahler
Manifolds
88
3.4.
Complex Vector Bundles and Chern Classes
92
3.5.
Line Bundles and Divisors
94
3.6.
The Calabi Conjecture and the Calabi-Yau Theorem
102
Chapter
4.
Fundamentals of Orbifolds
105
4.1.
Basic Definitions
105
4.2.
Orbisheaves and Orbibundles
108
4.3.
Groupoids, Orbifold Invariants, and Classifying Spaces
115
4.4.
Complex Orbifolds
123
4.5.
Weighted
Projective
Spaces
133
4.6.
Hypersurfaces in Weighted
Projective
Spaces
138
4.7. Seifert
Bundles
144
Chapter
5.
Kahler-Einstein Metrics
151
5.1.
Some Elementary Considerations
152
5.2.
The
Monge-Ampère
Problem and the Continuity Method
153
x
CONTENTS
5.3.
Obstructions in the Positive Case
160
5.4. Kahler
-Einstein Metrics on Hypersurfaces in CPiw)
162
•5.5.
Automorphisms and the Moduli Problem
173
Chapter
6.
Almost Contact and Contact Geometry
179
6.1.
Contact Structures
180
6.2.
Almost Contact Structures
190
6.3.
Almost Contact Metric Structures
195
6.4.
Contact Metric Structures
198
6.5.
Structures on Cones
200
Chapter
7.
K-Contact and Sasakian Structures
207
7.1.
Quasi-regularity and the Structure Theorems
207
7.2.
The Transverse Geometry of the Characteristic Foliation
214
7.3.
Curvature Properties of K-Contact and Sasakian Structures
219
7.4.
Topology of K-Contact and Sasakian Manifolds
229
7.5.
Sasakian Geometry and Algebraic Geometry
236
7.6.
New Sasakian Structures from Old
250
Chapter
8.
Symmetries and Sasakian Structures
257
8.1.
Automorphisms of Sasakian Structures and Isometries
257
8.2.
Deformation Classes of Sasakian Structures
265
8.3.
Homogeneous Sasakian Manifolds
272
8.4.
Symmetry Reduction and Moment Maps
276
8.5.
Contact and Sasakian Reduction
290
Chapter
9.
Links as Sasakian Manifolds
299
9.1.
Preliminaries
299
9.2.
Sasakian Structures and Weighted Homogeneous Polynomials
300
9.3.
The Milnor Fibration and the Topology of Links
302
9.4.
The Differential Topology of Links
312
9.5.
Positive Sasakian Structures on Links
319
9.6.
Links of Complete Intersections
326
Chapter
10.
Sasakian Geometry in Dimensions
3
and
5 329
10.1.
Sasakian Geometry in Dimension
3 329
10.2.
Sasakian Structures and the Topology of 5-Manifolds
335
10.3.
Sasakian Links in Dimension
5 352
10.4.
Regular Sasakian Structures on 5-Manifolds
360
Chapter
11.
Sasaki-Einstein Geometry
369
11.1.
Foundations of Sasaki-Einstein Geometry
370
11.2.
Extremal Sasakian Metrics
378
11.3.
Further Obstructions to Sasaki-Einstein Structures
382
11.4.
Sasaki-Einstein Metrics in Dimensions
5 388
11.5.
Sasaki-Einstein Metrics on Homotopy Spheres
403
11.6.
The Sasaki-Einstein semi-group
407
11.7.
Sasaki-Einstein Metrics in Dimensions
7
and Higher
409
11.8.
Sasakian-
rç-Einstein
Metrics
417
CONTENTS xi
Chapter
12. Quaternionic Kahler and Hyperkähler
Manifolds
421
12.1. Quaternionic
Geometry of
H
and HP™
422
12.2.
Quaternionic
Kahler
Metrics
428
12.3.
Positive Quaternionic
Kahler
Manifolds and Symmetries
434
12.4.
Quaternionic
Kahler
Reduction
438
12.5.
Compact Quaternionic
Kahler Orbifolds 443
12.6.
Hypercomplex and Hyperhermitian Structures
453
12.7. Hyperkähler
Manifolds
455
12.8. Hyperkähler
Quotients
458
12.9.
Toric
Hyperkähler
Metrics
461
12.10.
ALE Spaces and Other
Hyperkähler
Quotients
465
Chapter
13.
3-Sasakian Manifolds
473
13.1.
Almost Hypercontact Manifolds and 3-Sasakian Structures
474
13.2.
Basic Properties
478
13.3.
The Fundamental Foliations TT and Tq
480
13.4.
Homogeneous 3-Sasakian Manifolds
491
13.5.
3-Sasakian Cohomology
494
13.6.
Symmetry Reduction
499
13.7.
Toric 3-Sasakian Manifolds
506
13.8.
Cohomogeneity One 3-Sasakian 7-Manifolds
522
13.9-
Non-
Toric 3-Sasakian Manifolds in Dimension
11
and
15 525
Chapter
14.
Sasakian Structures, Killing Spinors, and Supersymmetry
529
14.1.
The Dirac Operator and Killing Spinors
529
14.2.
Real Killing Spinors, Holonomy, and Bar s Correspondence
533
14.3.
Geometries Associated with 3-Sasakian 7-manifolds
535
14.4.
Geometries Associated with Sasaki-Einstein 5-manifolds
543
14.5.
Geometric Structures on Manifolds and Supersymmetry
546
Appendix A
551
A.I. Preliminaries on Groupoids
551
A.
2.
The Classifying Space of a Topological Groupoid
555
Appendix
В
559
B.I. Reid s List of
КЗ
Surfaces as hypersurfaces in CP3(w)
559
B.2. Differential topology of 2k(S3
x
S4)
and 2fc(55
x S6)
560
8.3.
Tables of
Kähler-Einstein
metrics on hypersurfaces
CP(w)
561
8.
4.
Positive Breiskorn-Pham Links in Dimension
5 564
B.5. The Yau-Yu Links in Dimensions
5 567
Bibliography
569
Index
609
|
| adam_txt |
Contents
Preface
v
Introduction
1
Chapter
1.
Structures on Manifolds
9
1.1.
Sheaves and Sheaf Cohomology
9
1.2.
Principal and Associated Bundles
14
1.3.
Connections in Principal and Associated Vector Bundles
18
1.4.
G-Structures
23
1.5.
Pseudogroup Structures
36
1.6.
Group Actions on Manifolds
38
Chapter
2.
Foliations
51
2.1.
Examples of Foliations
51
2.2.
Haefliger Structures
52
2.3.
Leaf Holonomy and the Holonomy Groupoid
54
2.4.
Basic Cohomology
59
2.5.
Transverse Geometry
60
2.6.
Riemannian Flows
69
Chapter
3. Kahler
Manifolds
75
3.1.
Complex Manifolds and
Kahler
Metrics
76
3.2.
Curvature of
Kahler
Manifolds
82
3.3.
Hodge Theory on
Kahler
Manifolds
88
3.4.
Complex Vector Bundles and Chern Classes
92
3.5.
Line Bundles and Divisors
94
3.6.
The Calabi Conjecture and the Calabi-Yau Theorem
102
Chapter
4.
Fundamentals of Orbifolds
105
4.1.
Basic Definitions
105
4.2.
Orbisheaves and Orbibundles
108
4.3.
Groupoids, Orbifold Invariants, and Classifying Spaces
115
4.4.
Complex Orbifolds
123
4.5.
Weighted
Projective
Spaces
133
4.6.
Hypersurfaces in Weighted
Projective
Spaces
138
4.7. Seifert
Bundles
144
Chapter
5.
Kahler-Einstein Metrics
151
5.1.
Some Elementary Considerations
152
5.2.
The
Monge-Ampère
Problem and the Continuity Method
153
x
CONTENTS
5.3.
Obstructions in the Positive Case
160
5.4. Kahler
-Einstein Metrics on Hypersurfaces in CPiw)
162
•5.5.
Automorphisms and the Moduli Problem
173
Chapter
6.
Almost Contact and Contact Geometry
179
6.1.
Contact Structures
180
6.2.
Almost Contact Structures
190
6.3.
Almost Contact Metric Structures
195
6.4.
Contact Metric Structures
198
6.5.
Structures on Cones
200
Chapter
7.
K-Contact and Sasakian Structures
207
7.1.
Quasi-regularity and the Structure Theorems
207
7.2.
The Transverse Geometry of the Characteristic Foliation
214
7.3.
Curvature Properties of K-Contact and Sasakian Structures
219
7.4.
Topology of K-Contact and Sasakian Manifolds
229
7.5.
Sasakian Geometry and Algebraic Geometry
236
7.6.
New Sasakian Structures from Old
250
Chapter
8.
Symmetries and Sasakian Structures
257
8.1.
Automorphisms of Sasakian Structures and Isometries
257
8.2.
Deformation Classes of Sasakian Structures
265
8.3.
Homogeneous Sasakian Manifolds
272
8.4.
Symmetry Reduction and Moment Maps
276
8.5.
Contact and Sasakian Reduction
290
Chapter
9.
Links as Sasakian Manifolds
299
9.1.
Preliminaries
299
9.2.
Sasakian Structures and Weighted Homogeneous Polynomials
300
9.3.
The Milnor Fibration and the Topology of Links
302
9.4.
The Differential Topology of Links
312
9.5.
Positive Sasakian Structures on Links
319
9.6.
Links of Complete Intersections
326
Chapter
10.
Sasakian Geometry in Dimensions
3
and
5 329
10.1.
Sasakian Geometry in Dimension
3 329
10.2.
Sasakian Structures and the Topology of 5-Manifolds
335
10.3.
Sasakian Links in Dimension
5 352
10.4.
Regular Sasakian Structures on 5-Manifolds
360
Chapter
11.
Sasaki-Einstein Geometry
369
11.1.
Foundations of Sasaki-Einstein Geometry
370
11.2.
Extremal Sasakian Metrics
378
11.3.
Further Obstructions to Sasaki-Einstein Structures
382
11.4.
Sasaki-Einstein Metrics in Dimensions
5 388
11.5.
Sasaki-Einstein Metrics on Homotopy Spheres
403
11.6.
The Sasaki-Einstein semi-group
407
11.7.
Sasaki-Einstein Metrics in Dimensions
7
and Higher
409
11.8.
Sasakian-
rç-Einstein
Metrics
417
CONTENTS xi
Chapter
12. Quaternionic Kahler and Hyperkähler
Manifolds
421
12.1. Quaternionic
Geometry of
H"
and HP™
422
12.2.
Quaternionic
Kahler
Metrics
428
12.3.
Positive Quaternionic
Kahler
Manifolds and Symmetries
434
12.4.
Quaternionic
Kahler
Reduction
438
12.5.
Compact Quaternionic
Kahler Orbifolds 443
12.6.
Hypercomplex and Hyperhermitian Structures
453
12.7. Hyperkähler
Manifolds
455
12.8. Hyperkähler
Quotients
458
12.9.
Toric
Hyperkähler
Metrics
461
12.10.
ALE Spaces and Other
Hyperkähler
Quotients
465
Chapter
13.
3-Sasakian Manifolds
473
13.1.
Almost Hypercontact Manifolds and 3-Sasakian Structures
474
13.2.
Basic Properties
478
13.3.
The Fundamental Foliations TT and Tq
480
13.4.
Homogeneous 3-Sasakian Manifolds
491
13.5.
3-Sasakian Cohomology
494
13.6.
Symmetry Reduction
499
13.7.
Toric 3-Sasakian Manifolds
506
13.8.
Cohomogeneity One 3-Sasakian 7-Manifolds
522
13.9-
Non-
Toric 3-Sasakian Manifolds in Dimension
11
and
15 525
Chapter
14.
Sasakian Structures, Killing Spinors, and Supersymmetry
529
14.1.
The Dirac Operator and Killing Spinors
529
14.2.
Real Killing Spinors, Holonomy, and Bar's Correspondence
533
14.3.
Geometries Associated with 3-Sasakian 7-manifolds
535
14.4.
Geometries Associated with Sasaki-Einstein 5-manifolds
543
14.5.
Geometric Structures on Manifolds and Supersymmetry
546
Appendix A
551
A.I. Preliminaries on Groupoids
551
A.
2.
The Classifying Space of a Topological Groupoid
555
Appendix
В
559
B.I. Reid's List of
КЗ
Surfaces as hypersurfaces in CP3(w)
559
B.2. Differential topology of 2k(S3
x
S4)
and 2fc(55
x S6)
560
8.3.
Tables of
Kähler-Einstein
metrics on hypersurfaces
CP(w)
561
8.
4.
Positive Breiskorn-Pham Links in Dimension
5 564
B.5. The Yau-Yu Links in Dimensions
5 567
Bibliography
569
Index
609 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Boyer, Charles P. 1942- Galicki, Krzysztof 1958-2007 |
| author_GND | (DE-588)137447094 (DE-588)137447116 |
| author_facet | Boyer, Charles P. 1942- Galicki, Krzysztof 1958-2007 |
| author_role | aut aut |
| author_sort | Boyer, Charles P. 1942- |
| author_variant | c p b cp cpb k g kg |
| building | Verbundindex |
| bvnumber | BV023018297 |
| callnumber-first | Q - Science |
| callnumber-label | QA649 |
| callnumber-raw | QA649 |
| callnumber-search | QA649 |
| callnumber-sort | QA 3649 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 370 |
| ctrlnum | (OCoLC)140107626 (DE-599)DNB 2007023082 |
| 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 |
| discipline_str_mv | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV023018297 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T19:12:03Z |
| indexdate | 2024-07-09T21:09:05Z |
| institution | BVB |
| isbn | 9780198564959 |
| language | English |
| lccn | 2007023082 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016222421 |
| oclc_num | 140107626 |
| open_access_boolean | |
| owner | DE-384 DE-19 DE-BY-UBM DE-355 DE-BY-UBR |
| owner_facet | DE-384 DE-19 DE-BY-UBM DE-355 DE-BY-UBR |
| physical | XI, 613 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Oxford University Press |
| record_format | marc |
| series2 | Oxford mathematical monographs Oxford Science Publications |
| spelling | Boyer, Charles P. 1942- Verfasser (DE-588)137447094 aut Sasakian geometry Charles P. Boyer and Krzysztof Galicki 1. publ. Oxford Oxford University Press 2008 XI, 613 S. txt rdacontent n rdamedia nc rdacarrier Oxford mathematical monographs Oxford Science Publications Includes bibliographical references and index Sasakian manifolds Geometry Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Riemannsche Geometrie (DE-588)4128462-8 gnd rswk-swf Kontaktmannigfaltigkeit (DE-588)4669522-9 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 s Riemannsche Geometrie (DE-588)4128462-8 s DE-604 Kontaktmannigfaltigkeit (DE-588)4669522-9 s 1\p DE-604 Galicki, Krzysztof 1958-2007 Verfasser (DE-588)137447116 aut http://www.loc.gov/catdir/toc/ecip0719/2007023082.html Table of contents only Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016222421&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Boyer, Charles P. 1942- Galicki, Krzysztof 1958-2007 Sasakian geometry Sasakian manifolds Geometry Mannigfaltigkeit (DE-588)4037379-4 gnd Riemannsche Geometrie (DE-588)4128462-8 gnd Kontaktmannigfaltigkeit (DE-588)4669522-9 gnd |
| subject_GND | (DE-588)4037379-4 (DE-588)4128462-8 (DE-588)4669522-9 |
| title | Sasakian geometry |
| title_auth | Sasakian geometry |
| title_exact_search | Sasakian geometry |
| title_exact_search_txtP | Sasakian geometry |
| title_full | Sasakian geometry Charles P. Boyer and Krzysztof Galicki |
| title_fullStr | Sasakian geometry Charles P. Boyer and Krzysztof Galicki |
| title_full_unstemmed | Sasakian geometry Charles P. Boyer and Krzysztof Galicki |
| title_short | Sasakian geometry |
| title_sort | sasakian geometry |
| topic | Sasakian manifolds Geometry Mannigfaltigkeit (DE-588)4037379-4 gnd Riemannsche Geometrie (DE-588)4128462-8 gnd Kontaktmannigfaltigkeit (DE-588)4669522-9 gnd |
| topic_facet | Sasakian manifolds Geometry Mannigfaltigkeit Riemannsche Geometrie Kontaktmannigfaltigkeit |
| url | http://www.loc.gov/catdir/toc/ecip0719/2007023082.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016222421&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT boyercharlesp sasakiangeometry AT galickikrzysztof sasakiangeometry |