High Quality Content by WIKIPEDIA articles! In differential geometry, a G2-structure is an important type of G-structure that can be defined on a smooth manifold. If M is a smooth manifold of dimension seven, then a G2-structure is a reduction of structure group of the frame bundle of M to the compact, exceptional Lie group G2. The property of being a G2-manifold is much stronger than that of admitting a G2-structure. Indeed, a G2-manifold is a manifold with a G2-structure which is torsion-free. The letter "G" occurring in the phrases "G-structure" and "G2-structure" refers to different things. In the first case, G-structures take their name from the fact that arbitrary Lie groups are typically denoted with the letter "G". On the other hand, the letter "G" in "G2" comes from the fact that the its Lie algebra is the seventh type ("G" being the seventh letter of the alphabet) in the classification of complex simple Lie algebras by Elie Cartan.

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