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What (who) is (G,X)-manifold - definition
(G,X)-manifold
MATHEMATICAL CONCEPT
(G,X)-structure
In geometry, if X is a manifold with an action of a topological group G by analytical diffeomorphisms, the notion of a (G, X)-structure on a topological space is a way to formalise it being locally isomorphic to X with its G-invariant structure; spaces with a (G, X)-structure are always manifolds and are called (G, X)-manifolds. This notion is often used with G being a Lie group and X a homogeneous space for G.
G2 manifold
SEVEN-DIMENSIONAL RIEMANNIAN MANIFOLD WITH HOLONOMY GROUP CONTAINED IN G2
Joyce manifold; G2-manifold
In differential geometry, a G2 manifold is a seven-dimensional Riemannian manifold with holonomy group contained in G2. The group G_2 is one of the five exceptional simple Lie groups.
Differentiable manifold
MANIFOLD UPON WHICH IT IS POSSIBLE TO PERFORM CALCULUS (ANY DIFFERENTIABLITY CLASS)
Differential manifold; Smooth manifold; Smooth manifolds; Differentiable manifolds; Manifold/rewrite/differentiable manifold; Differental manifold; Sheaf of smooth functions; Geometric structure; Ambient manifold; Non-smoothable manifold; Curved manifold
In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a vector space to allow one to apply calculus. Any manifold can be described by a collection of charts (atlas).
Wikipedia
(G,X)-manifold
In geometry, if X is a manifold with an action of a topological group G by analytical diffeomorphisms, the notion of a (G, X)-structure on a topological space is a way to formalise it being locally isomorphic to X with its G-invariant structure; spaces with a (G, X)-structure are always manifolds and are called (G, X)-manifolds. This notion is often used with G being a Lie group and X a homogeneous space for G.
