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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} .

Reduction of the structure group, Overview & Integrability conditions and flat G-structures