About: G-structure on a manifold

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In differential geometry, a G-structure on an n-manifold M, for a given structure group G, is a principal 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.

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rdfs:label	G-structure on a manifold (en) 구조 다양체 (ko) G-结构 (zh)
rdfs:comment	미분기하학에서 구조 다양체(영어: -structure manifold)는 그 접다발이 어떤 리 군의 작용을 갖춘 매끄러운 다양체이다. (ko) 在微分几何中，对一个给定的结构群 G，n 维流形 M 上一个 G-结构是 M 的切标架丛 FM（或 GL(M)）的一个 G-。 G-结构的概念包括了许多流形上其它结构，其中一些是用张量场定义的。例如，对正交群，一个 O(n)-结构定义了一个黎曼度量；而对特殊线性群，一个 SL(n,R)-结构就是一个体积形式；对平凡群，一个 {e}-结构由流形的一个绝对平行化组成。一些流形上的结构，比如複结构，，或凯勒结构，都是 G-结构带上附加的。物理学中的术语是规范群。 (zh) In differential geometry, a G-structure on an n-manifold M, for a given structure group G, is a principal 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. (en)
dcterms:subject	Differential geometry Structures on manifolds
Wikipage page ID	1277699 (xsd:integer)
Wikipage revision ID	1119448717 (xsd:integer)
Link from a Wikipage to another Wikipage	Pushforward (differential) Quaternion Vector-valued differential form Torsion (differential geometry) Torsion of connection Almost complex manifold Almost symplectic manifold Vector space Volume form Inclusion map Indefinite orthogonal group Lie derivative Trivial group Differential geometry Structures on manifolds Connection form General linear group Tangent bundle Pullback (differential geometry) Pullback bundle Classifying space Frobenius theorem (differential topology) Connection (principal bundle) Connection (vector bundle) Symplectic structure Almost complex Complex manifold Functor Subgroup Symplectic group Calabi–Yau manifold Maximal compact subgroup Adjoint bundle Whitney sum G2-structure Jet group Linear complex structure Affine space Fiber bundle Foliation Diffeomorphism Frame bundle Deformation retract Journal of Geometry and Physics Moving frame Orthonormal frame Tensor field Riemannian metric Group (mathematics) Rigid transformation Covering space Block matrix Homotopy lifting property Smoothness Differential geometry Associated bundle Automorphism group Manifold Bulletin of the AMS Fibration Induced representation Kähler manifold Orthogonal group Cartan's equivalence method Special linear group Vector bundle Principal bundle Subbundle Space (mathematics) Solder form Parallelizable manifold Orientable Spin structure Pseudo Riemannian metric Transformation group Transition map Orientation (manifold) 2-form Nijenhuis tensor Almost Kähler manifold Almost complex structure Real vector bundle Integrability condition Complex general linear group Spin manifold Structure group
Link from a Wikipage to an external page	https://books.google.com/books%3Fid=mCyvdD1zLwQC&pg=PA123
sameAs	G-structure on a manifold G-structure on a manifold G-structure on a manifold

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