Differential geometry and analysis on CR manifolds:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2006
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| Series: | Progress in mathematics
246 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 463 - 482 |
| Physical Description: | XIV, 487 S. 25 cm |
| ISBN: | 0817643885 9780817643881 |
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| 100 | 1 | |a Dragomir, Sorin |d 1955- |e Verfasser |0 (DE-588)140382186 |4 aut | |
| 245 | 1 | 0 | |a Differential geometry and analysis on CR manifolds |c Sorin Dragomir ; Giuseppe Tomassini |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2006 | |
| 300 | |a XIV, 487 S. |c 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Progress in mathematics |v 246 | |
| 500 | |a Literaturverz. S. 463 - 482 | ||
| 650 | 4 | |a CR submanifolds | |
| 650 | 4 | |a Differentiable manifolds | |
| 650 | 4 | |a Geometry, Differential | |
| 650 | 0 | 7 | |a Differentialgeometrie |0 (DE-588)4012248-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Cauchy-Riemannsche Mannigfaltigkeit |0 (DE-588)4147400-4 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Tomassini, Giuseppe |e Verfasser |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 0-8176-4483-0 |
| 830 | 0 | |a Progress in mathematics |v 246 |w (DE-604)BV000004120 |9 246 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-014833464 | ||
Record in the Search Index
| _version_ | 1804135408620011520 |
|---|---|
| adam_text | Contents
Preface
їх
CR Manifolds
................................................ 1
1.1
CR
manifolds
................................................
З
1.1.1
CR structures
.........................................
З
1.1.2
The
Levi
form
......................................... 5
1.1.3
Characteristic directions on
nondegenerate CR
manifolds
..... 8
1.1.4
CR geometry and contact Riemannian geometry
............ 10
1.1.5
The
Heisenberg
group
.................................. 11
1.1.6
Embeddable CR manifolds
.............................. 14
1.1.7
CR Lie algebras and CR Lie groups
....................... 18
1.1.8
Twister CR manifolds
.................................. 21
1.2
The Tanaka-Webster connection
................................ 25
1.3
Local computations
........................................... 31
1.3.1
Christoffel symbols
.................................... 32
1.3.2
The pseudo-Hermitian torsion
............................ 36
1.3.3
The volume form
...................................... 43
1.4
The curvature theory
.......................................... 46
1.4.1
Pseudo-Hermitian
Ricci
and scalar curvature
............... 50
1.4.2
The curvature forms
Ω^
................................. 51
1.4.3
Pseudo-Hermitian sectional curvature
..................... 58
1.5
The Chern tensor field
......................................... 60
1.6
CR structures as G-structures
.................................. 68
1.6.1
Integrability
........................................... 70
1.6.2
Nondegeneracy
........................................ 72
1.7
The tangential Cauchy-Riemann complex
........................ 73
1.7.1
The tangential Cauchy-Riemann complex
................. 73
1.7.2
CR-holomorphic bundles
................................ 82
1.7.3
The
FröHcher
spectral sequence
.......................... 84
1.7.4
A long exact sequence
.................................. 94
1.7.5
Bott
obstructions
....................................... 96
vi
Contents
1.7.6
The Kohn-Rossi Laplacian
.............................. 99
1.8
The group of CR automorphisms
................................
Ю6
2
The Fefferman Metric
.........................................
109
2.1
The sub-Laplacian
............................................
HI
2.2
The canonical bundle
.........................................119
2.3
The Fefferman metric
.........................................122
2.4
A CR invariant
...............................................135
2.5
The wave operator
............................................140
2.6
Curvature of Fefferman s metric
................................141
2.7
Pontryagin forms
.............................................142
2.8
The extrinsic approach
........................................147
2.8.1
The
Monge-Ampère
equation
............................147
2.8.2
The Fefferman metric
...................................150
2.8.3
Obstructions to global embeddability
......................151
3
The CRYamabe Problem
...................................... 157
3.1
The Cayley transform
.........................................161
3.2
Normal coordinates
...........................................165
3.3
A Sobolev-type lemma
........................................176
3.4
Embedding results
............................................193
3.5
Regularity results
.............................................196
3.6
Existence of extremals
........................................200
3.7
Uniqueness and open problems
.................................205
3.8
The weak maximum principle for
Afe
............................207
4
Pseudoharmonic Maps
.........................................211
4.1
CR and pseudoharmonic maps
..................................212
4.2
A geometric interpretation
.....................................215
4.3
The variational approach
......................................218
4.4 Hörmander
systems and
harmonicity
............................231
4.4.1 Hörmander
systems
....................................233
4.4.2
Subelliptic harmonic morphisms
.........................236
4.4.3
The relationship to hyperbolic PDEs
......................239
4.4.4
Weak harmonic maps from CfH,,)
........................242
4.5
Generalizations of pseudoharmonicity
...........................246
4.5.1
The first variation formula
...............................248
4.5.2
Pseudoharmonic morphisms
.............................252
4.5.3
The geometric interpretation of F-pseudoharmonicity
.......255
4.5.4
Weak subelliptic F-harmonic maps
.......................256
5
Pseudo-Einsteinian Manifolds
...................................275
5.1
The local problem
............................................275
5.2
The divergence formula
.......................................279
5.3
CR-pluriharmonic functions
....................................280
Contents
vii
5.4
More local theory
............................................294
5.5
Topological obstructions
.......................................296
5.5.1
The first Chern class of TUO(M)
..........................296
5.5.2
The traceless
Ricci
tensor
...............................299
5.5.3
The Lee class
.........................................301
5.6
The global problem
...........................................304
5.7
The Lee conjecture
...........................................312
5.7.1
Quotients of the
Heisenberg
group by properly discontinuous
groups of CR automorphisms
............................313
5.7.2
Regular strictly pseudoconvex CR manifolds
...............318
5.7.3
The
Bockstein
sequence
................................320
5.7.4
The tangent sphere bundle
...............................321
5.8
Pseudo-Hermitian holonomy
...................................329
5.9
Quaternionic Sasakian manifolds
...............................331
5.10
Homogeneous pseudo-Einsteinian manifolds
......................341
Pseudo-Hermitian Immersions
..................................345
6.1
The theorem of H. Jacobowitz
..................................347
6.2
The second fundamental form
..................................351
6.3
CR immersions into Hn+k
.....................................356
6.4
Pseudo-Einsteinian structures
..................................361
6.4.1
CR-pluriharmonic functions and the Lee class
..............361
6.4.2
Consequences of the embedding equations
.................364
6.4.3
The first Chern class of the normal bundle
.................369
Quasiconformal Mappings
......................................377
7.1
The complex dilatation
........................................377
7.2
^-quasiconformal maps
.......................................384
7.3
The tangential Beltrami equations
...............................385
7.3.1
Contact transformations of
Н„
...........................388
7.3.2
The tangential Beltrami equation on Hi
...................394
7.4
Symplectomorphisms
.........................................398
7.4.1
Fefferman s formula and boundary behavior of
symplectomorphisms
...................................398
7.4.2
Dilatation of symplectomorphisms and the Beltrami equations
401
7.4.3
Boundary values of solutions to the Beltrami system
.........403
7.4.4
A theorem of P.
Libermann..............................403
7.4.5
Extensions of contact deformations
.......................405
Yang-Mills Fields on CR Manifolds
..............................407
8.1
Canonical S-connections
......................................407
8.2
Inhomogeneous Yang-Mills equations
...........................410
8.3
Applications
.................................................412
8.3.1
Trivial line bundles
.....................................414
8.3.2
Locally trivial line bundles
..............................414
viii Contents
8.3.3
Canonical bundles
.....................................416
8.4
Various differential operators
...................................418
8.5
Curvature of S-connections
....................................421
9
Spectral Geometry
............................................423
9.1
Commutation formulas
........................................423
9.2
A lower bound for
λ]
.........................................427
9.2.1
A Bochner-type formula
................................430
9.2.2
Two integral identities
..................................431
9.2.3
A. Greenleaf s theorem
.................................434
9.2.4
A lower bound on the first eigenvalue of a Folland-Stein
operator
..............................................439
9.2.5
Z. Jiaqing and Y. Hongcang s theorem on CR manifolds
......441
A Parametrix for D^
...............................................445
References
.......................................................463
Index
............................................................483
|
| adam_txt |
Contents
Preface
їх
CR Manifolds
. 1
1.1
CR
manifolds
.
З
1.1.1
CR structures
.
З
1.1.2
The
Levi
form
. 5
1.1.3
Characteristic directions on
nondegenerate CR
manifolds
. 8
1.1.4
CR geometry and contact Riemannian geometry
. 10
1.1.5
The
Heisenberg
group
. 11
1.1.6
Embeddable CR manifolds
. 14
1.1.7
CR Lie algebras and CR Lie groups
. 18
1.1.8
Twister CR manifolds
. 21
1.2
The Tanaka-Webster connection
. 25
1.3
Local computations
. 31
1.3.1
Christoffel symbols
. 32
1.3.2
The pseudo-Hermitian torsion
. 36
1.3.3
The volume form
. 43
1.4
The curvature theory
. 46
1.4.1
Pseudo-Hermitian
Ricci
and scalar curvature
. 50
1.4.2
The curvature forms
Ω^
. 51
1.4.3
Pseudo-Hermitian sectional curvature
. 58
1.5
The Chern tensor field
. 60
1.6
CR structures as G-structures
. 68
1.6.1
Integrability
. 70
1.6.2
Nondegeneracy
. 72
1.7
The tangential Cauchy-Riemann complex
. 73
1.7.1
The tangential Cauchy-Riemann complex
. 73
1.7.2
CR-holomorphic bundles
. 82
1.7.3
The
FröHcher
spectral sequence
. 84
1.7.4
A long exact sequence
. 94
1.7.5
Bott
obstructions
. 96
vi
Contents
1.7.6
The Kohn-Rossi Laplacian
. 99
1.8
The group of CR automorphisms
.
Ю6
2
The Fefferman Metric
.
109
2.1
The sub-Laplacian
.
HI
2.2
The canonical bundle
.119
2.3
The Fefferman metric
.122
2.4
A CR invariant
.135
2.5
The wave operator
.140
2.6
Curvature of Fefferman's metric
.141
2.7
Pontryagin forms
.142
2.8
The extrinsic approach
.147
2.8.1
The
Monge-Ampère
equation
.147
2.8.2
The Fefferman metric
.150
2.8.3
Obstructions to global embeddability
.151
3
The CRYamabe Problem
. 157
3.1
The Cayley transform
.161
3.2
Normal coordinates
.165
3.3
A Sobolev-type lemma
.176
3.4
Embedding results
.193
3.5
Regularity results
.196
3.6
Existence of extremals
.200
3.7
Uniqueness and open problems
.205
3.8
The weak maximum principle for
Afe
.207
4
Pseudoharmonic Maps
.211
4.1
CR and pseudoharmonic maps
.212
4.2
A geometric interpretation
.215
4.3
The variational approach
.218
4.4 Hörmander
systems and
harmonicity
.231
4.4.1 Hörmander
systems
.233
4.4.2
Subelliptic harmonic morphisms
.236
4.4.3
The relationship to hyperbolic PDEs
.239
4.4.4
Weak harmonic maps from CfH,,)
.242
4.5
Generalizations of pseudoharmonicity
.246
4.5.1
The first variation formula
.248
4.5.2
Pseudoharmonic morphisms
.252
4.5.3
The geometric interpretation of F-pseudoharmonicity
.255
4.5.4
Weak subelliptic F-harmonic maps
.256
5
Pseudo-Einsteinian Manifolds
.275
5.1
The local problem
.275
5.2
The divergence formula
.279
5.3
CR-pluriharmonic functions
.280
Contents
vii
5.4
More local theory
.294
5.5
Topological obstructions
.296
5.5.1
The first Chern class of TUO(M)
.296
5.5.2
The traceless
Ricci
tensor
.299
5.5.3
The Lee class
.301
5.6
The global problem
.304
5.7
The Lee conjecture
.312
5.7.1
Quotients of the
Heisenberg
group by properly discontinuous
groups of CR automorphisms
.313
5.7.2
Regular strictly pseudoconvex CR manifolds
.318
5.7.3
The
Bockstein
sequence
.320
5.7.4
The tangent sphere bundle
.321
5.8
Pseudo-Hermitian holonomy
.329
5.9
Quaternionic Sasakian manifolds
.331
5.10
Homogeneous pseudo-Einsteinian manifolds
.341
Pseudo-Hermitian Immersions
.345
6.1
The theorem of H. Jacobowitz
.347
6.2
The second fundamental form
.351
6.3
CR immersions into Hn+k
.356
6.4
Pseudo-Einsteinian structures
.361
6.4.1
CR-pluriharmonic functions and the Lee class
.361
6.4.2
Consequences of the embedding equations
.364
6.4.3
The first Chern class of the normal bundle
.369
Quasiconformal Mappings
.377
7.1
The complex dilatation
.377
7.2
^-quasiconformal maps
.384
7.3
The tangential Beltrami equations
.385
7.3.1
Contact transformations of
Н„
.388
7.3.2
The tangential Beltrami equation on Hi
.394
7.4
Symplectomorphisms
.398
7.4.1
Fefferman's formula and boundary behavior of
symplectomorphisms
.398
7.4.2
Dilatation of symplectomorphisms and the Beltrami equations
401
7.4.3
Boundary values of solutions to the Beltrami system
.403
7.4.4
A theorem of P.
Libermann.403
7.4.5
Extensions of contact deformations
.405
Yang-Mills Fields on CR Manifolds
.407
8.1
Canonical S-connections
.407
8.2
Inhomogeneous Yang-Mills equations
.410
8.3
Applications
.412
8.3.1
Trivial line bundles
.414
8.3.2
Locally trivial line bundles
.414
viii Contents
8.3.3
Canonical bundles
.416
8.4
Various differential operators
.418
8.5
Curvature of S-connections
.421
9
Spectral Geometry
.423
9.1
Commutation formulas
.423
9.2
A lower bound for
λ]
.427
9.2.1
A Bochner-type formula
.430
9.2.2
Two integral identities
.431
9.2.3
A. Greenleaf's theorem
.434
9.2.4
A lower bound on the first eigenvalue of a Folland-Stein
operator
.439
9.2.5
Z. Jiaqing and Y. Hongcang's theorem on CR manifolds
.441
A Parametrix for D^
.445
References
.463
Index
.483 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Dragomir, Sorin 1955- Tomassini, Giuseppe |
| author_GND | (DE-588)140382186 |
| author_facet | Dragomir, Sorin 1955- Tomassini, Giuseppe |
| author_role | aut aut |
| author_sort | Dragomir, Sorin 1955- |
| author_variant | s d sd g t gt |
| building | Verbundindex |
| bvnumber | BV021618364 |
| callnumber-first | Q - Science |
| callnumber-label | QA641 |
| callnumber-raw | QA641 |
| callnumber-search | QA641 |
| callnumber-sort | QA 3641 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 370 |
| ctrlnum | (OCoLC)67775224 (DE-599)BVBBV021618364 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| id | DE-604.BV021618364 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T14:52:50Z |
| indexdate | 2024-07-09T20:40:02Z |
| institution | BVB |
| isbn | 0817643885 9780817643881 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014833464 |
| oclc_num | 67775224 |
| open_access_boolean | |
| owner | DE-824 DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-83 DE-11 DE-188 |
| owner_facet | DE-824 DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-83 DE-11 DE-188 |
| physical | XIV, 487 S. 25 cm |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Dragomir, Sorin 1955- Verfasser (DE-588)140382186 aut Differential geometry and analysis on CR manifolds Sorin Dragomir ; Giuseppe Tomassini Boston [u.a.] Birkhäuser 2006 XIV, 487 S. 25 cm txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 246 Literaturverz. S. 463 - 482 CR submanifolds Differentiable manifolds Geometry, Differential Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Cauchy-Riemannsche Mannigfaltigkeit (DE-588)4147400-4 gnd rswk-swf Cauchy-Riemannsche Differentialgleichungen (DE-588)4147397-8 gnd rswk-swf Cauchy-Riemannsche Mannigfaltigkeit (DE-588)4147400-4 s Differentialgeometrie (DE-588)4012248-7 s DE-604 Cauchy-Riemannsche Differentialgleichungen (DE-588)4147397-8 s Tomassini, Giuseppe Verfasser aut Erscheint auch als Online-Ausgabe 0-8176-4483-0 Progress in mathematics 246 (DE-604)BV000004120 246 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014833464&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dragomir, Sorin 1955- Tomassini, Giuseppe Differential geometry and analysis on CR manifolds Progress in mathematics CR submanifolds Differentiable manifolds Geometry, Differential Differentialgeometrie (DE-588)4012248-7 gnd Cauchy-Riemannsche Mannigfaltigkeit (DE-588)4147400-4 gnd Cauchy-Riemannsche Differentialgleichungen (DE-588)4147397-8 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4147400-4 (DE-588)4147397-8 |
| title | Differential geometry and analysis on CR manifolds |
| title_auth | Differential geometry and analysis on CR manifolds |
| title_exact_search | Differential geometry and analysis on CR manifolds |
| title_exact_search_txtP | Differential geometry and analysis on CR manifolds |
| title_full | Differential geometry and analysis on CR manifolds Sorin Dragomir ; Giuseppe Tomassini |
| title_fullStr | Differential geometry and analysis on CR manifolds Sorin Dragomir ; Giuseppe Tomassini |
| title_full_unstemmed | Differential geometry and analysis on CR manifolds Sorin Dragomir ; Giuseppe Tomassini |
| title_short | Differential geometry and analysis on CR manifolds |
| title_sort | differential geometry and analysis on cr manifolds |
| topic | CR submanifolds Differentiable manifolds Geometry, Differential Differentialgeometrie (DE-588)4012248-7 gnd Cauchy-Riemannsche Mannigfaltigkeit (DE-588)4147400-4 gnd Cauchy-Riemannsche Differentialgleichungen (DE-588)4147397-8 gnd |
| topic_facet | CR submanifolds Differentiable manifolds Geometry, Differential Differentialgeometrie Cauchy-Riemannsche Mannigfaltigkeit Cauchy-Riemannsche Differentialgleichungen |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014833464&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
| work_keys_str_mv | AT dragomirsorin differentialgeometryandanalysisoncrmanifolds AT tomassinigiuseppe differentialgeometryandanalysisoncrmanifolds |