Geometry of groups of transformations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English French |
| Published: |
Leyden
Noordhoff
1977
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 234 S. |
| ISBN: | 9028605061 |
Staff View
MARC
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| 100 | 1 | |a Lichnerowicz, André |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Géométrie des groupes de transformations |
| 245 | 1 | 0 | |a Geometry of groups of transformations |c André Lichnerowicz. Transl. and ed. by Michael Cole |
| 264 | 1 | |a Leyden |b Noordhoff |c 1977 | |
| 300 | |a XIV, 234 S. | ||
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Record in the Search Index
| _version_ | 1804116920895537152 |
|---|---|
| adam_text | CONTENTS
CHAPTER I
HARMONIC FORMS AND CURVATURE OF A RIEMANNIAN MANIFOLD
1:1 EXPLICIT CALCULATION OF Aa 1
:2 EXPLICIT CALCULATION OF A|a|2 3
r3 Results On Orientable compact manifolds 4
: 4 locally Convex hypersurfaces 7
:5 case Of Compact Pseudokahlerian manifolds ... 9
f6 a formula concerning the curvature tensor ... 10
CHAPTER II
INFINITESIMAL TRANSFORMATIONS ON A DIFFERENTIABLE MANIFOLD
2;7 derivation and antiderivation 13
:8 examples Of derivations and antiderivations ... 15
:9 one parameter local Group Of local
transformations 16
•10 Infinitesimal transforms of vector Valued forms 18
• 11 the fundamental Formula 19
,12 Bracket Of Two Infinitesimal Transformations... 20
:13 vector fields projectable under a
differentiable mapping 21
:14 infinitesimal. transforms of forms of e(vm) ... 23
:15 the infinitesimal transform of a tensor: rules. 25
:16 infinitesimal transformations and bracket of
two vector fields 26
ix
x contents
2:17 infinitesimal transform of the structure
Operator 27
:18 Invariant Local Sections 28
:19 Introduction of a linear connection 30
:20 calculation Of lie derivatives 32
:2l infinitesimal Transformation and absolute
Differentiation 33
:22 tensor densities 34
CHAPTER III
GROUPS OF TRANSFORMATIONS AND HOMOGENEOUS SPACES
3 1: GENERAL PROPERTIES
3 1.23 groups Of Transformations 36
.24 elements Invariant Under A transformation or
group of Transformations 38
.25 homogeneous spaces 39
.26 normal coordinates and geodesic polar
coordinates for a manifold with a linear
Connection 42
.27 basic vector Fields for a linear Connection ... 45
.28 affine transformations 48
.29 Affine Infinitesimal transformations on a
Complete Manifold 50
.30 homogeneous spaces with an invariant linear
Connection 51
3 2: REDUCTIVE HOMOGENEOUS SPACES AND REDUCTIVE ALGEBRAS
3 2.31 reductive homogeneous spaces 52
.32 examples of reductive homogeneous spaces. ... 54
.33 curvature and torsion of the canonical
Connection 55
.34 Covariant derivation In The Canonical Linear
Connection 57
.35 the Restricted holonomy group Of the canonical
Connection 58
.36 Other invariant Linear Connections On a
Reductive homogeneous space 59
.37 the cartan connection 62
.38 Connection Defined by an Invariant
non degenerate quadratic form 63
.39 Naturally reductive riemannian Homogeneous
Spaces 65
CONTENTS xi
3 2.40 the notion Of Locally reductive manifold. ... 67
.41 a form of the bianchi identity in terms of the
curvature 68
.42 locally Reductive Manifolds and Reductive
homogeneous spaces 69
.43 reductive lie algebras 73
.44 homogeneous spaces in which h leaves no non zero
Vector invariant 76
CHAPTER IV
AFFINE TRANSFORMATIONS AND ISOMETRIES
4*1: GLOBAL TRANSFORMATIONS OF RIEMANNIAN MANIFOLDS
4 1.45 generalities about transformations 78
.46 study of affine transformation of manifolds
With An Euclidian Connection 80
.47 Study of homotheties Of Complete riemannian
manifolds 81
.48 affine transformations and reducible riemannian
manifolds 83
.49 case Where The Manifold Is Simply connected ... 85
.50 affine transformations of complete simply
connected manifolds 86
.51 case of non Simply Connected Manifolds 88
4 2: STUDY AND INTERVENTION OF ALMOST HERMITIAN MANIFOLDS
4 2.52 A LEMMA 90
.53 Study Of the Connected normaliser of a for
manifold with an euclidian connection 92
.54 affine transformations of certain almost
hermitian manifolds 94
.55 The case Of complete pseudoka hlerian Manifolds. 95
4 3: AFFINE INFINITESIMAL TRANSFORMATIONS AND HOLONOMY
4 3.56 THE ALGEBRA OF AFFINE INFINITESIMAL
TRANSFORMATIONS 96
.57 INTERPRETATION OF THE ENDOMORPHISMS Ax 97
.58 CURVATURE AND AFFINE INFINITESIMAL
TRANSFORMATIONS 100
.59 THE GROUP KXU) 101
xii CONTENTS
4*3.60 Case of a transitive Algebra Of Affine
Infinitesimal transformations 102
.61 case of a homogeneous space with an invariant
Linear Connection 103
.62 Tensors invariant and with Vanishing covariant
Derivative On a homogeneous Space with An
Invariant linear connection 106
.63 Cartan Connection Of a reductive homogeneous
Space 108
.64 holonomy and infinitesimal isometries for a
Riemannian Manifold Ill
.65 case Of a compact Riemannian manifold 114
.66 Case of A naturally Reductive riemannian
Homogeneous space 115
.67 case Where The group G is compact 117
4«4: RIEMANNIAN HOMOGENEOUS SPACES AND REDUCIBILITY
4 4.68 FIRST RESULTS ON RIEMANNIAN HOMOGENEOUS SPACES. 118
.69 A theorem On Irreducibility for a simple
GROUP G 121
.70 A lemma On The Groups Of Displacements of an
Euclidian Space 122
.71 Case Of a riemannian homogeneous space With
Semi Simple Group G 123
.72 A lemma On Reductive homogeneous Spaces 123
.73 riemannian homogeneous space admitting
Reductive Space Structure 125
.74 Case where h Has Inequivalent representations.. 129
CHAPTER V
CONFORMAL TRANSFORMATIONS AND ANALYTIC TRANSFORMATIONS
IN THE COMPACT CASE
5 1: CONFORMAL TRANSFORMATIONS OF A RIEMANNIAN MANIFOLD
5 1.75 invariance of a tensor density 133
.76 local Scalar Product and Global Scalar Product. 135
.77 identities Involving t(a) 135
.78 characterisation of conformal infinitesimal
transformations in the compact case 137
.79 Affine Transformations Of a compact riemannian
manifold 139
.80 invariance of harmonic forms 139
CONTENTS xiii
5 1.81 case Of An Euclidian connection with
irreducible holonomy group 140
.82 case Of the first canonical connection Of An
almost hermitian manifold 141
.83 some results involving conformal infinitesimal
transformations 142
.84 a result concerning the eigenvalues of a on
1 FORMS 143
.85 conformal transformations and isometries for
Einstein Spaces 146
.86 Case where The largest Connected Group Of
isometries is transitive and semi simple ... 149
5 2: ANALYTIC TRANSFORMATIONS OF COMPACT KAHLERIAN MANIFOLDS
5*2.87 resume Of complex Analytic and ka hlerian
manifolds 152
.88 notion Of Analytic transformation 154
.89 Identities Concerning Analytic infinitesimal
transformations 156
.90 conformal transformations. of a compact
kahlerian manifold 158
.91 holonomy and analytic transformations 159
.92 An Algebra Of Analytic infinitesimal
Transformations 164
.93 case of a manifold with constant scalar
Curvature 165
.94 introduction of the operators d , d , 6 , 6 ... 167
.95 Representation Of Analytic transformations Of
certain kahlerian manifolds 170
.96 Case Of, Isometries 172
.97 A system Of Fundamental Functions For a
K JLERIAN HOMOGENEOUS SPACE WITH SEMI SIMPLE
G 176
.98 Study Of An embedding 176
.99 Manifolds With r = constant for which Ao(V2n)
IS OF MAXIMUM DIMENSION 179
.100 MANIFOLDS FOR WHICH Io(V2n) Is °F MAXIMUM
DIMENSION 180
CHAPTER VI
SYMMETRIC SPACES
6:101 notion Of symmetric homogeneous Space 183
:102 symmetry with respect to a point 186
xiv CONTENTS
6:103 INVARIANCE OF THE CANONICAL CONNECTION UNDER
SYMMETRY 189
:104 INVARIANCE OF TENSORS: APPLICATIONS 191
; 105 TRANSVECTION 192
tlO6 AN EXAMPLE OF A SYMMETRIC HOMOGENEOUS SPACE ... 194
:107 HOLONOMY OF A SYMMETRIC SPACE 195
?1O8 Symmetric Spaces with G Semi Simple 196
?109 SYMMETRIC SPACES WITH #0 IRREDUCIBLE 197
?11O Locally Symmetric Manifolds 199
till A Theorem In the case Where G is Semi Simple... 201
bibliography 205
Subject Index 209
list Of symbols 231
|
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| author | Lichnerowicz, André |
| author_facet | Lichnerowicz, André |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 350 SK 370 |
| ctrlnum | (OCoLC)3225393 (DE-599)BVBBV002518133 |
| dewey-full | 516/.36 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516/.36 |
| dewey-search | 516/.36 |
| dewey-sort | 3516 236 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002518133 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:46:11Z |
| institution | BVB |
| isbn | 9028605061 |
| language | English French |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001619694 |
| oclc_num | 3225393 |
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| owner_facet | DE-91G DE-BY-TUM DE-384 DE-703 DE-824 DE-19 DE-BY-UBM DE-706 DE-83 DE-11 DE-188 |
| physical | XIV, 234 S. |
| publishDate | 1977 |
| publishDateSearch | 1977 |
| publishDateSort | 1977 |
| publisher | Noordhoff |
| record_format | marc |
| spelling | Lichnerowicz, André Verfasser aut Géométrie des groupes de transformations Geometry of groups of transformations André Lichnerowicz. Transl. and ed. by Michael Cole Leyden Noordhoff 1977 XIV, 234 S. txt rdacontent n rdamedia nc rdacarrier Geometry, Differential Transformation groups Geometrie (DE-588)4020236-7 gnd rswk-swf Transformation Mathematik (DE-588)4060637-5 gnd rswk-swf Transformationsgruppe (DE-588)4127386-2 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Transformation Mathematik (DE-588)4060637-5 s Differentialgeometrie (DE-588)4012248-7 s DE-604 Transformationsgruppe (DE-588)4127386-2 s Geometrie (DE-588)4020236-7 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001619694&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lichnerowicz, André Geometry of groups of transformations Geometry, Differential Transformation groups Geometrie (DE-588)4020236-7 gnd Transformation Mathematik (DE-588)4060637-5 gnd Transformationsgruppe (DE-588)4127386-2 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4020236-7 (DE-588)4060637-5 (DE-588)4127386-2 (DE-588)4012248-7 |
| title | Geometry of groups of transformations |
| title_alt | Géométrie des groupes de transformations |
| title_auth | Geometry of groups of transformations |
| title_exact_search | Geometry of groups of transformations |
| title_full | Geometry of groups of transformations André Lichnerowicz. Transl. and ed. by Michael Cole |
| title_fullStr | Geometry of groups of transformations André Lichnerowicz. Transl. and ed. by Michael Cole |
| title_full_unstemmed | Geometry of groups of transformations André Lichnerowicz. Transl. and ed. by Michael Cole |
| title_short | Geometry of groups of transformations |
| title_sort | geometry of groups of transformations |
| topic | Geometry, Differential Transformation groups Geometrie (DE-588)4020236-7 gnd Transformation Mathematik (DE-588)4060637-5 gnd Transformationsgruppe (DE-588)4127386-2 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Geometry, Differential Transformation groups Geometrie Transformation Mathematik Transformationsgruppe Differentialgeometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001619694&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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