Open Access
January 2009 Geometric structures on G2 and Spin (7)-manifolds
Jae-Hyouk Lee, Naichung Conan Leung
Adv. Theor. Math. Phys. 13(1): 1-31 (January 2009).


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.


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Jae-Hyouk Lee. Naichung Conan Leung. "Geometric structures on G2 and Spin (7)-manifolds." Adv. Theor. Math. Phys. 13 (1) 1 - 31, January 2009.


Published: January 2009
First available in Project Euclid: 21 January 2009

MathSciNet: MR2471851

Rights: Copyright © 2009 International Press of Boston

Vol.13 • No. 1 • January 2009
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