Riemannian geometry of contact and symplectic manifolds:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2002
|
| Series: | Progress in mathematics
203 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 260 S. graph. Darst. |
| ISBN: | 0817642617 3764342617 |
Staff View
MARC
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| 245 | 1 | 0 | |a Riemannian geometry of contact and symplectic manifolds |c David E. Blair |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2002 | |
| 300 | |a XII, 260 S. |b graph. Darst. | ||
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| 650 | 7 | |a GEOMETRIA RIEMANNIANA |2 larpcal | |
| 650 | 7 | |a GEOMETRIA SIMPLETICA |2 larpcal | |
| 650 | 4 | |a Riemann, Géométrie de | |
| 650 | 4 | |a Variétés de contact | |
| 650 | 4 | |a Variétés symplectiques | |
| 650 | 4 | |a Contact manifolds | |
| 650 | 4 | |a Geometry, Riemannian | |
| 650 | 4 | |a Symplectic manifolds | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
1 Symplectic Manifolds 1
1.1 Definitions and examples 1
1.2 Lagrangian submanifolds 5
1.3 The Darboux Weinstein theorems 7
1.4 Symplectomorphisms 9
2 Principal S^bundles 11
2.1 The set of principal S1 bundles as a group 11
2.2 Connections on a principal bundle 14
3 Contact Manifolds 17
3.1 Definitions 17
3.2 Examples 20
3.2.1 M2n+1 20
3.2.2 Rn+1 x PW1 21
3.2.3 M2n+1 C M2n+2 with TmM2n+1 D {0} = 0 21
3.2.4 T{M, TXM 22
3.2.5 T*MxR 22
3.2.6 T3 23
3.2.7 T5 23
3.2.8 Overtwisted contact structures 24
3.2.9 Contact circles 25
3.3 The Boothby Wang fibration 26
3.4 The Weinstein conjecture 28
viii Contents
4 Associated Metrics 31
4.1 Almost complex and almost contact structures 31
4.2 Polarization and associated metrics 34
4.3 Polarization of metrics as a projection 38
4.3.1 Some linear algebra 39
4.3.2 Results on the set A 41
4.4 Action of symplectic and contact transformations 45
4.5 Examples of almost contact metric manifolds 48
4.5.1 R2n+1 48
4.5.2 M2n+1 C M2n+2 almost complex 49
4.5.3 5s c 56 50
4.5.4 The Boothby Wang fibration 52
4.5.5 M2n x R 53
4.5.6 Parallelizable manifolds 53
5 Integral Submanifolds and Contact Transformations 55
5.1 Integral submanifolds 55
5.2 Contact transformations 57
5.3 Examples of integral submanifolds 59
5.3.1 Sn c S2n+1 59
5.3.2 T2 c 5s 59
5.3.3 Legendre curves and Whitney spheres 60
i 5.3.4 Lift of a Lagrangian submanifold 62
6 Sasakian and Cosymplectic Manifolds 63
6.1 Normal almost contact structures 63
6.2 The tensor field h 67
6.3 Definition of a Sasakian manifold 69
6.4 CR manifolds 72
6.5 Cosymplectic manifolds and remarks on the Sasakian definition 77
6.6 Products of almost contact manifolds 79
6.7 Examples 81
6.7.1 M2n+1 81
6.7.2 Principal circle bundles 81
6.7.3 A non normal almost contact structure on S5 83
6.7.4 M2n+1 c M2n+2 85
6.7.5 Brieskorn manifolds 85
6.8 Topology 87
7 Curvature of Contact Metric Manifolds 91
7.1 Basic curvature properties 91
7.2 Curvature of contact metric manifolds 95
Contents ix
7.3 ^ sectional curvature 110
7.4 Examples of Sasakian space forms 114
7.4.1 S2n+1 114
7.4.2 M2n+1 114
7.4.3 B xl 115
7.5 Locally (^ symmetric spaces 115
8 Submanifolds of Kahler and Sasakian Manifolds 121
8.1 Invariant submanifolds 121
8.2 Lagrangian and integral submanifolds 124
8.3 Legendre curves 133
9 Tangent Bundles and Tangent Sphere Bundles 137
9.1 Tangent bundles 137
9.2 Tangent sphere bundles 142
9.3 Geometry of vector bundles 148
9.4 Normal bundles 150
10 Curvature Functionals on Spaces of Associated Metrics 157
10.1 Introduction to critical metric problems 157
10.2 The * scalar curvature 162
10.3 The integral of Ric(£) 166
10.4 The Webster scalar curvature 170
10.5 A gauge invariant 173
10.6 The Abbena metric as a critical point 174
11 Negative ^ sectional Curvature 177
11.1 Special Directions in the contact subbundle 177
11.2 Anosov flows 178
11.3 Conformally Anosov flows 184
12 Complex Contact Manifolds 189
12.1 Complex contact manifolds and associated metrics 189
12.2 Examples of complex contact manifolds 193
12.2.1 Complex Heisenberg group 193
12.2.2 Odd dimensional complex projective space 194
12.2.3 Twistor spaces 196
12.2.4 The complex Boothby Wang fibration 198
12.2.5 3 dimensional homogeneous examples 200
12.2.6 Cn+1 x CPn(16) 200
12.3 Normality of complex contact manifolds 202
12.4 G// sectional curvature 204
x Contents
12.5 The set of associated metrics and integral functional 206
12.6 Holomorphic Legendre curves 209
12.7 The Calabi (Veronese) imbeddings as integral submanifolds
ofCP2n+i 212
13 3 Sasakian Manifolds 215
13.1 3 Sasakian manifolds 215
13.2 Integral submanifolds 223
Bibliography 227
Subject Index 253
Author Index 257
|
| any_adam_object | 1 |
| author | Blair, David E. |
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| ctrlnum | (OCoLC)48256138 (DE-599)BVBBV013990114 |
| 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 |
| format | Book |
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| id | DE-604.BV013990114 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:55:39Z |
| institution | BVB |
| isbn | 0817642617 3764342617 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009575558 |
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| physical | XII, 260 S. graph. Darst. |
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| publisher | Birkhäuser |
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| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Blair, David E. Verfasser aut Riemannian geometry of contact and symplectic manifolds David E. Blair Boston [u.a.] Birkhäuser 2002 XII, 260 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 203 GEOMETRIA RIEMANNIANA larpcal GEOMETRIA SIMPLETICA larpcal Riemann, Géométrie de Variétés de contact Variétés symplectiques Contact manifolds Geometry, Riemannian Symplectic manifolds Riemannsche Geometrie (DE-588)4128462-8 gnd rswk-swf Symplektische Mannigfaltigkeit (DE-588)4290704-4 gnd rswk-swf Kontaktmannigfaltigkeit (DE-588)4669522-9 gnd rswk-swf Riemannsche Geometrie (DE-588)4128462-8 s Symplektische Mannigfaltigkeit (DE-588)4290704-4 s Kontaktmannigfaltigkeit (DE-588)4669522-9 s DE-604 Progress in mathematics 203 (DE-604)BV000004120 203 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009575558&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Blair, David E. Riemannian geometry of contact and symplectic manifolds Progress in mathematics GEOMETRIA RIEMANNIANA larpcal GEOMETRIA SIMPLETICA larpcal Riemann, Géométrie de Variétés de contact Variétés symplectiques Contact manifolds Geometry, Riemannian Symplectic manifolds Riemannsche Geometrie (DE-588)4128462-8 gnd Symplektische Mannigfaltigkeit (DE-588)4290704-4 gnd Kontaktmannigfaltigkeit (DE-588)4669522-9 gnd |
| subject_GND | (DE-588)4128462-8 (DE-588)4290704-4 (DE-588)4669522-9 |
| title | Riemannian geometry of contact and symplectic manifolds |
| title_auth | Riemannian geometry of contact and symplectic manifolds |
| title_exact_search | Riemannian geometry of contact and symplectic manifolds |
| title_full | Riemannian geometry of contact and symplectic manifolds David E. Blair |
| title_fullStr | Riemannian geometry of contact and symplectic manifolds David E. Blair |
| title_full_unstemmed | Riemannian geometry of contact and symplectic manifolds David E. Blair |
| title_short | Riemannian geometry of contact and symplectic manifolds |
| title_sort | riemannian geometry of contact and symplectic manifolds |
| topic | GEOMETRIA RIEMANNIANA larpcal GEOMETRIA SIMPLETICA larpcal Riemann, Géométrie de Variétés de contact Variétés symplectiques Contact manifolds Geometry, Riemannian Symplectic manifolds Riemannsche Geometrie (DE-588)4128462-8 gnd Symplektische Mannigfaltigkeit (DE-588)4290704-4 gnd Kontaktmannigfaltigkeit (DE-588)4669522-9 gnd |
| topic_facet | GEOMETRIA RIEMANNIANA GEOMETRIA SIMPLETICA Riemann, Géométrie de Variétés de contact Variétés symplectiques Contact manifolds Geometry, Riemannian Symplectic manifolds Riemannsche Geometrie Symplektische Mannigfaltigkeit Kontaktmannigfaltigkeit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009575558&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
| work_keys_str_mv | AT blairdavide riemanniangeometryofcontactandsymplecticmanifolds |