G-structure on a manifold

In differential geometry, a G-structure on an n {\displaystyle n} -manifold M {\displaystyle M} , for a given structure group G {\displaystyle G} , is a principal G {\displaystyle G} -subbundle of the tangent frame bundle F M {\displaystyle {\text{F}}M} (or GL ⁡ ( M ) {\displaystyle \operatorname {GL} (M)} ) of M {\displaystyle M} . The notion of G {\displaystyle G} -structures includes various classical structures that can be defined on manifolds, which in some cases are tensor fields.

Source: Wikipedia — G-structure on a manifold (CC BY-SA 4.0)

G-structure on a manifold

In differential geometry, a G-structure on an n {\displaystyle n} -manifold M {\displaystyle M} , for a given structure group G {\displaystyle G} , is a principal G {\displaystyle G} -subbundle of the tangent frame bundle F M {\displaystyle {\text{F}}M} (or GL ⁡ ( M ) {\displaystyle \operatorname {GL} (M)} ) of M {\displaystyle M} . The notion of G {\displaystyle G} -structures includes various classical structures that can be defined on manifolds, which in some cases are tensor fields.

Source: Wikipedia "G-structure on a manifold" · CC BY-SA 4.0

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