Diffeomorphisms of 7-Manifolds with Closed G_2-Structure

Details Diffeomorphisms of 7-Manifolds with Closed G_2-Structure Diffeomorphisms of 7-Manifolds with Closed G_2-Structure

2011-12-05

arxiv.org/abs/1112.0832v2

Mathematics

Differential Geometry

10 pages; LaTex; Ver. 2 fixes typos and errors in addition to updating the introduction and references

Scientific paper

We study the geometry of 7-manifolds equipped with a closed G_2-structure. We introduce G_2 vector fields and Rochesterian vector fields which are analogues of symplectic vector fields and Hamiltonian vector fields respectively. In fact, the spaces X_{G_2} and X_{Roc} of G_2 and Rochesterian vector fields admit the structure of Lie algebras where the bracket operation is induced from the standard Lie bracket on the algebra of vector fields. Further, the space of Rochesterian 1-forms associated to the space of Rochesterian vector fields also admits the structure of a Lie algebra; finally, we show that there is a Lie algebra homomorphism between the Rochesterian 1-forms and Rochesterian vector fields and prove a result about the kernel of this homomorphism.

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