This article studies the geometry of moduli spaces of G2-manifolds, associative cycles, coassociative cycles and deformed Donaldson–Thomas bundles. We introduce natural symmetric cubic tensors and differential forms on these moduli spaces. They correspond to Yukawa couplings and correlation functions in M-theory.
We expect that the Yukawa coupling characterizes (co-)associative fibrations on these manifolds. We discuss the Fourier transformation along such fibrations and the analog of the Strominger–Yau–Zaslow mirror conjecture for G2-manifolds.
We also discuss similar structures and transformations for Spin(7)- manifolds.
"Geometric structures on G2 and Spin (7)-manifolds." Adv. Theor. Math. Phys. 13 (1) 1 - 31, January 2009.