Hyunjoo Cho, Sema Salur, Albert J. Todd
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.
View original:
http://arxiv.org/abs/1112.0832
No comments:
Post a Comment