| Titre : |
Théorie des G-structures: le probmème d'equivalence |
| Type de document : |
texte imprimé |
| Auteurs : |
Pierre MOLINO, Auteur ; A. DOLD, Editeur commercial ; B. ECKMANN, Editeur commercial |
| Editeur : |
Springer-Verlag |
| Année de publication : |
1977 |
| Collection : |
lecture notes in mathématics |
| Importance : |
163 p. |
| Format : |
25 cm. |
| ISBN/ISSN/EAN : |
978-3-540-08246-0 |
| Note générale : |
Bibliog. |
| Langues : |
Français (fre) |
| Catégories : |
MATHÉMATIQUES:Algébre
|
| Index. décimale : |
04-03 Algébre |
| Résumé : |
In differential geometry, a G-structure on an n-manifold M, for a given structure group[1] G, is a G-subbundle of the tangent frame bundle FM (or GL(M)) of M.
The notion of G-structures includes various classical structures that can be defined on manifolds, which in some cases are tensor fields. For example, for the orthogonal group, an O(n)-structure defines a Riemannian metric, and for the special linear group an SL(n,R)-structure is the same as a volume form. For the trivial group, an {e}-structure consists of an absolute parallelism of the manifold.
Generalising this idea to arbitrary principal bundles on topological spaces, one can ask if a principal {\displaystyle G}G-bundle over a group {\displaystyle G}G "comes from" a subgroup {\displaystyle H}H of {\displaystyle G}G. This is called reduction of the structure group (to {\displaystyle H}H).
Several structures on manifolds, such as a complex structure, a symplectic structure, or a Kähler structure, are G-structures with an additional integrability condition.
Table of contents:
Introduction
Theorie Des Jets
G-structures
Structures d'Ordre Superieur
Pseudogroupes et Γ-structures
Presque-structures et problème d'équivalence
Techniques générales 1
Techniques générales 2
Techniques générales 3
Structures plates; modèles standard
Théorème d'équivalence 1
Théorème d'équivalence 2
Généralisations et applications |
Théorie des G-structures: le probmème d'equivalence [texte imprimé] / Pierre MOLINO, Auteur ; A. DOLD, Editeur commercial ; B. ECKMANN, Editeur commercial . - Springer-Verlag, 1977 . - 163 p. ; 25 cm.. - ( lecture notes in mathématics) . ISBN : 978-3-540-08246-0 Bibliog. Langues : Français ( fre)
| Catégories : |
MATHÉMATIQUES:Algébre
|
| Index. décimale : |
04-03 Algébre |
| Résumé : |
In differential geometry, a G-structure on an n-manifold M, for a given structure group[1] G, is a G-subbundle of the tangent frame bundle FM (or GL(M)) of M.
The notion of G-structures includes various classical structures that can be defined on manifolds, which in some cases are tensor fields. For example, for the orthogonal group, an O(n)-structure defines a Riemannian metric, and for the special linear group an SL(n,R)-structure is the same as a volume form. For the trivial group, an {e}-structure consists of an absolute parallelism of the manifold.
Generalising this idea to arbitrary principal bundles on topological spaces, one can ask if a principal {\displaystyle G}G-bundle over a group {\displaystyle G}G "comes from" a subgroup {\displaystyle H}H of {\displaystyle G}G. This is called reduction of the structure group (to {\displaystyle H}H).
Several structures on manifolds, such as a complex structure, a symplectic structure, or a Kähler structure, are G-structures with an additional integrability condition.
Table of contents:
Introduction
Theorie Des Jets
G-structures
Structures d'Ordre Superieur
Pseudogroupes et Γ-structures
Presque-structures et problème d'équivalence
Techniques générales 1
Techniques générales 2
Techniques générales 3
Structures plates; modèles standard
Théorème d'équivalence 1
Théorème d'équivalence 2
Généralisations et applications |
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