Riemannian geometry of contact and symplectic manifolds:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2010
|
| Edition: | 2. ed. |
| Series: | Progress in mathematics
203 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 343 S. graph. Darst. |
| ISBN: | 9780817649586 |
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MARC
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| 100 | 1 | |a Blair, David E. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Riemannian geometry of contact and symplectic manifolds |c David E. Blair |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York, NY |b Springer |c 2010 | |
| 300 | |a XV, 343 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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Record in the Search Index
| _version_ | 1804143254535405568 |
|---|---|
| adam_text | Contents
Preface
to Second Edition
vii
Preface to the First Edition
ix
1
Symplectic Manifolds
1
1.1
Definitions and examples
................... 1
1.2
Lagrangian submanifolds
................... 6
1.3
The Darboux—
Weinstein
theorems
............. 9
1.4
Symplectomorphisms
..................... 11
2
Principal ^-bundles
15
2.1
The set of principal ^-bundles as a group
......... 15
2.2
Connections on a principal bundle
............. 19
3
Contact Manifolds
23
3.1
Definitions
........................... 23
3.2
Examples
........................... 27
3.2.1
R2n+1
......................... 27
3.2.2
Rn+1
χ
PW1
..................... 28
3.2.3
M2n+1
С
R2n+2 with TmM2n+1
П
{0} = 0..... 28
3.2.4
Unit and projectivized tangent and cotangent
bundles
........................ 29
3.2.5
T*M xE
....................... 30
xii Contents
3.2.6
Tori
..........................
ЗО
3.2.7
Overtwisted contact
structures
........... 32
3.2.8
S2 x S1
........................ 34
3.2.9
Contact
circles....................
35
3.3
The Boothby-Wang fibration
................ 36
3.4
The
Weinstein
conjecture
.................. 38
4
Associated Metrics
41
4.1
Almost complex and almost contact structures
...... 41
4.2
Polarization and associated metrics
............. 45
4.3
Polarization of metrics as a projection
........... 49
4.3.1
Some linear algebra
................. 50
4.3.2
Results on the set
Λ
................. 53
4.4
Action of symplectic and contact transformations
..... 57
4.5
Examples of almost contact metric manifolds
....... 60
4.5.1
m2n+1
......................... 60
4.5.2
M2n+1
С
M2n+2 almost complex
.......... 61
4.5.3
S5 c
S6........................
63
4.5.4
The Boothby-Wang fibration
............ 64
4.5.5
M2n xR
....................... 66
4.5.6
Parallelizable manifolds
............... 67
5
Integral Submanifolds and Contact Transformations
69
5.1
Integral submanifolds
.................... 69
5.2
Contact transformations
................... 71
5.3
Examples of integral submanifolds
............. 74
5.3.1
Sn
с
52n+1
...................... 74
5.3.2
T2 CS5
........................ 74
5.3.3
Legendre curves and Whitney spheres
....... 75
5.3.4
Lift of a Lagrangian foliation, Legendre foliations
. 77
6
Sasakian and Cosymplectic Manifolds
79
6.1
Normal almost contact structures
.............. 79
6.2
The tensor field
h
....................... 83
6.3
Definition of a Sasakian manifold
.............. 86
6.4
CR-manifolds
......................... 89
6.5
Cosymplectic manifolds and remarks on the Sasakian
definition
........................... 95
6.6
Products of almost contact manifolds
............ 97
Contents xiii
6.7
Examples
...........................100
6.7.1 R2n+1......................... 100
6.7.2 Principal
circle bundles
............... 100
6.7.3
A
nonnormal
almost contact structure on S5
... 102
6.7.4
M2n+1
с М2п+2
................... 104
6.7.5
Brieskorn manifolds
................. 104
6.8
Some early topology
..................... 106
7
Curvature of Contact Metric Manifolds 111
7.1
Basic curvature properties
..................
Ill
7.2
Curvature of contact metric manifolds
........... 116
7.3
The
(к,
M)-manifolds
..................... 123
7.4
Sasakian Einstein manifolds
................. 130
7.5
Locally symmetric contact metric manifolds
........ 132
7.6
Conformally flat contact metric manifolds
......... 133
7.7
^-sectional curvature
..................... 137
7.8
Examples of Sasakian space forms
............. 141
7.8.1
52n+1
......................... 142
7.8.2
Ш2п+1
......................... 142
7.8.3 ß xl........................ 142
7.9
Locally
tè-symmetric
spaces
................. 143
8
Submanifolds of
Kahler
and Sasakian Manifolds
151
8.1
Invariant submanifolds
....................151
8.2
Lagrangian and integral submanifolds
...........155
9
Tangent Bundles and Tangent Sphere Bundles
169
9.1
Tangent bundles
....................... 169
9.2
Tangent sphere bundles
................... 175
9.3
Geometry of vector bundles
................. 183
9.4
Normal bundles
........................ 186
9.5
The geodesic flow on the projectivized tangent bundle
. . 191
10
Curvature Functionals on Spaces of Associated Metrics
195
10.1
Introduction to critical metric problems
..........195
10.2
The »-scalar curvature
....................201
10.3
The integral of
Hieß)....................206
10.3.1
H-contact
manifolds
.................211
10.4
The Webster scalar curvature
................212
xiv Contents
10.5
A gauge invariant
.......................215
10.6
The Abbena metric as a critical point
...........217
11
Negative ^-sectional Curvature
219
11.1
Special directions in the contact subbundle
........219
11.2
Anosov flows
.........................221
11.3
Conformally Anosov flows
..................227
12
Complex Contact Manifolds
233
12.1
Complex contact manifolds and associated metrics
.... 233
12.2
Examples of complex contact manifolds
..........238
12.2.1
Complex
Heisenberg
group
.............238
12.2.2
Odd-dimensional complex
projective
space
.....240
12.2.3
Twistor spaces
....................242
12.2.4
The Complex Boothby-Wang fibration
.......244
12.2.5
S-dimenskmal homogeneous examples
.......246
12.2.6
Complex contact Lie groups
.............247
12.2.7
C *1
χ
CPn(16)
...................248
12.2.8
cosz3dzx +sin z3dz2
.................250
12.3
Normality of complex contact manifolds
..........250
12.4
Cur-sectional curvature
...................252
12.5
The set of associated metrics and integral functionals
. . . 255
12.6
Holomorphic Legendre curves
................257
12.7
The Calabi (Veronese) embeddings as integral
submanifolds of CP2 4 1
...................260
13
Additional Topics in Complex Geometry
265
13.1
Partial and holomorphic hyperbolicity
........... 265
13.2
Projectivized holomorphic bundles
............. 268
13.3
The complex geodesic flow
.................. 271
13.4
Complex almost contact metric structure on
Рт
...... 278
13.4.1
A complex contact structure with nonintegrable
vertical subbundle
.................. 280
13.5
Special directions on complex contact manifolds and the
Lie group SL(2,C)
...................... 283
Contents xv
14 3-Sasakian
Manifolds
291
14.1 3-Sasakian
manifolds.....................
291
14.2 Integral submanifolds ....................299
Bibliography
303
Subject
Index 335
Author
Index 339
|
| any_adam_object | 1 |
| author | Blair, David E. |
| author_facet | Blair, David E. |
| author_role | aut |
| author_sort | Blair, David E. |
| author_variant | d e b de deb |
| building | Verbundindex |
| bvnumber | BV036637913 |
| classification_rvk | SK 370 |
| ctrlnum | (OCoLC)705768525 (DE-599)BVBBV036637913 |
| 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 | 2. ed. |
| format | Book |
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| id | DE-604.BV036637913 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:44:44Z |
| institution | BVB |
| isbn | 9780817649586 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020557598 |
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| owner_facet | DE-20 DE-11 DE-355 DE-BY-UBR DE-188 DE-83 |
| physical | XV, 343 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Blair, David E. Verfasser aut Riemannian geometry of contact and symplectic manifolds David E. Blair 2. ed. New York, NY Springer 2010 XV, 343 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 203 Symplektische Mannigfaltigkeit (DE-588)4290704-4 gnd rswk-swf Riemannsche Geometrie (DE-588)4128462-8 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 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020557598&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 Symplektische Mannigfaltigkeit (DE-588)4290704-4 gnd Riemannsche Geometrie (DE-588)4128462-8 gnd Kontaktmannigfaltigkeit (DE-588)4669522-9 gnd |
| subject_GND | (DE-588)4290704-4 (DE-588)4128462-8 (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 | Symplektische Mannigfaltigkeit (DE-588)4290704-4 gnd Riemannsche Geometrie (DE-588)4128462-8 gnd Kontaktmannigfaltigkeit (DE-588)4669522-9 gnd |
| topic_facet | Symplektische Mannigfaltigkeit Riemannsche Geometrie Kontaktmannigfaltigkeit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020557598&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
| work_keys_str_mv | AT blairdavide riemanniangeometryofcontactandsymplecticmanifolds |