Riemannian holonomy groups and calibrated geometry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Oxford University Press
2008
|
| Edition: | 1. publ., reprinted |
| Series: | Oxford graduate texts in mathematics
12 |
| Subjects: | |
| Online Access: | Contributor biographical information Publisher description Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | ix, 303 p. ill. 24 cm |
| ISBN: | 9780199215607 0199215596 9780199215591 |
Staff View
MARC
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| 100 | 1 | |a Joyce, Dominic D. |d 1968- |e Verfasser |0 (DE-588)1043994483 |4 aut | |
| 245 | 1 | 0 | |a Riemannian holonomy groups and calibrated geometry |c Dominic D. Joyce |
| 250 | |a 1. publ., reprinted | ||
| 264 | 1 | |a Oxford |b Oxford University Press |c 2008 | |
| 300 | |a ix, 303 p. |b ill. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Oxford graduate texts in mathematics |v 12 | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Geometry, Riemannian | |
| 650 | 4 | |a Holonomy groups | |
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Record in the Search Index
| _version_ | 1804145591523999744 |
|---|---|
| adam_text | Contents
Preface
v
1
Background material
1
1.1
Exterior
forms on manifolds
1
1.2
Introduction to analysis
4
1.3
Introduction to elliptic operators
7
1.4
Regularity of solutions of elliptic equations
12
1.5
Existence of solutions of linear elliptic equations
16
2
Introduction to connections, curvature and holonomy groups
19
2.1
Bundles, connections and curvature
19
2.2
Vector bundles, connections and holonomy groups
24
2.3
Holonomy groups and principal bundles
28
2.4
Holonomy groups and curvature
30
2.5
Connections on the tangent bundle, and torsion
32
2.6
G-structures and intrinsic torsion
36
3
Riemannian holonomy groups
40
3.1
Introduction to Riemannian holonomy groups
40
3.2
Reducible Riemannian manifolds
44
3.3
Riemannian symmetric spaces
48
3.4
The classification of Riemannian holonomy groups
52
3.5
Holonomy groups, exterior forms and cohomology
56
3.6
Spinors and holonomy groups
61
4
Calibrated geometry
65
4.1
Minimal submanifolds and calibrated submanifolds
65
4.2
Calibrated geometry and Riemannian holonomy groups
67
4.3
Classification of calibrations on Rn
69
4.4
Geometric measure theory and tangent cones
72
5 Kahler
manifolds
75
5.1
Introduction to complex manifolds
76
5.2
Tensors on complex manifolds
79
5.3
Holomorphic vector bundles
81
5.4
Introduction to
Kahler
manifolds
82
5.5 Kahler
potentials
83
5.6
Curvature of
Kahler
manifolds
84
5.7
Exterior forms on
Kahler
manifolds
85
VII
viii CONTENTS
5.8
Complex
algebraic varieties
88
5.9
Singular varieties, resolutions, and deformations
92
5.10
Line bundles and divisors
96
6
The Calabi Conjecture
100
6.1
Reformulating the Calabi Conjecture
101
6.2
Overview of the proof of the Calabi Conjecture
103
6.3
Calculations at a point
106
6.4
The proof of Theorem
С
1 109
6.5
The proof of Theorem C2
116
6.6
The proof of Theorem C3
118
6.7
The proof of Theorem C4
120
6.8
A discussion of the proof
120
7
Calabi-Yau manifolds
122
7.1
Ricci-fiat
Kahler
manifolds and Calabi-Yau manifolds
123
7.2
Crêpant
resolutions, small resolutions, and flops
127
7.3
Crêpant
resolutions of quotient singularities
129
7.4
Complex orbifolds
133
7.5
Crêpant
resolutions of orbifolds
137
7.6
Complete intersections
140
7.7
Deformations of Calabi-Yau manifolds
144
8
Special Lagrangian geometry
146
8.1
Special Lagrangian submanifolds in Cm
146
8.2
Constructing examples of SL m-folds in Cm
150
8.3
SL cones and Asymptotically Conical SL m-folds
157
8.4
SL m-folds in (almost) Calabi-Yau m-folds
165
8.5
SL m-folds with isolated conical singularities
170
9
Mirror symmetry and the SYZ Conjecture
178
9.1
String theory and mirror symmetry for dummies
178
9.2
Early mathematical formulations of mirror symmetry
181
9.3
Kontsevich s homological mirror symmetry proposal
183
9.4
The SYZ Conjecture
191
10 Hyperkähler
and quaternionic
Kahler
manifolds
201
10.1
An introduction to
hyperkähler
geometry
201
10.2 Hyperkähler
ALE spaces
205
10.3
КЗ
surfaces
208
10.4
Higher-dimensional compact
hyperkähler
manifolds
214
10.5
Quaternionic
Kahler
manifolds
219
10.6
Other topics in quaternionic geometry
222
11
The exceptional holonomy groups
227
11.1
The holonomy group G2
227
11.2
Topological properties of compact
G2
-manifolds
230
CONTENTS ix
11.3
Constructing compact G?
-manifolds
233
11.4
The holonomy group Spin(7)
239
11.5
Topological properties of compact Spin(7)-manifolds
242
11.6
Constructing compact Spin(7)-manifolds
245
11.7
Further reading on the exceptional holonomy groups
252
12
Associative, coassociative and Cayley submanifolds
254
12.1
Associative 3-folds and coassociative 4-folds in
Ш7
254
12.2
Constructing associative and coassociative fc-folds in R7
259
12.3
Associative
3-
and coassociative 4-folds in G^-manifolds
264
12.4
Cayley 4-folds in R8
272
12.5
Cayley 4-folds in Spin(7)-manifolds
274
References
278
Index
298
|
| any_adam_object | 1 |
| author | Joyce, Dominic D. 1968- |
| author_GND | (DE-588)1043994483 |
| author_facet | Joyce, Dominic D. 1968- |
| author_role | aut |
| author_sort | Joyce, Dominic D. 1968- |
| author_variant | d d j dd ddj |
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| bvnumber | BV037314726 |
| callnumber-first | Q - Science |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 370 |
| ctrlnum | (OCoLC)76935627 (DE-599)BVBBV037314726 |
| dewey-full | 516.373 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.373 |
| dewey-search | 516.373 |
| dewey-sort | 3516.373 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ., reprinted |
| format | Book |
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| id | DE-604.BV037314726 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T23:21:53Z |
| institution | BVB |
| isbn | 9780199215607 0199215596 9780199215591 |
| language | English |
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| oclc_num | 76935627 |
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| owner | DE-703 |
| owner_facet | DE-703 |
| physical | ix, 303 p. ill. 24 cm |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Oxford University Press |
| record_format | marc |
| series | Oxford graduate texts in mathematics |
| series2 | Oxford graduate texts in mathematics |
| spelling | Joyce, Dominic D. 1968- Verfasser (DE-588)1043994483 aut Riemannian holonomy groups and calibrated geometry Dominic D. Joyce 1. publ., reprinted Oxford Oxford University Press 2008 ix, 303 p. ill. 24 cm txt rdacontent n rdamedia nc rdacarrier Oxford graduate texts in mathematics 12 Includes bibliographical references and index Geometry, Riemannian Holonomy groups Riemannsche Geometrie (DE-588)4128462-8 gnd rswk-swf Holonomiegruppe (DE-588)4160487-8 gnd rswk-swf Riemannsche Geometrie (DE-588)4128462-8 s Holonomiegruppe (DE-588)4160487-8 s DE-604 Oxford graduate texts in mathematics 12 (DE-604)BV011416591 12 http://www.loc.gov/catdir/enhancements/fy0737/2007276857-b.html Contributor biographical information http://www.loc.gov/catdir/enhancements/fy0737/2007276857-d.html Publisher description Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022469061&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Joyce, Dominic D. 1968- Riemannian holonomy groups and calibrated geometry Oxford graduate texts in mathematics Geometry, Riemannian Holonomy groups Riemannsche Geometrie (DE-588)4128462-8 gnd Holonomiegruppe (DE-588)4160487-8 gnd |
| subject_GND | (DE-588)4128462-8 (DE-588)4160487-8 |
| title | Riemannian holonomy groups and calibrated geometry |
| title_auth | Riemannian holonomy groups and calibrated geometry |
| title_exact_search | Riemannian holonomy groups and calibrated geometry |
| title_full | Riemannian holonomy groups and calibrated geometry Dominic D. Joyce |
| title_fullStr | Riemannian holonomy groups and calibrated geometry Dominic D. Joyce |
| title_full_unstemmed | Riemannian holonomy groups and calibrated geometry Dominic D. Joyce |
| title_short | Riemannian holonomy groups and calibrated geometry |
| title_sort | riemannian holonomy groups and calibrated geometry |
| topic | Geometry, Riemannian Holonomy groups Riemannsche Geometrie (DE-588)4128462-8 gnd Holonomiegruppe (DE-588)4160487-8 gnd |
| topic_facet | Geometry, Riemannian Holonomy groups Riemannsche Geometrie Holonomiegruppe |
| url | http://www.loc.gov/catdir/enhancements/fy0737/2007276857-b.html http://www.loc.gov/catdir/enhancements/fy0737/2007276857-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022469061&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011416591 |
| work_keys_str_mv | AT joycedominicd riemannianholonomygroupsandcalibratedgeometry |