Geometric structures on G2 and Spin(7)-manifolds
Differential Geometry
2007-12-14 v2 Mathematical Physics
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.math/0202045,
title = {Geometric structures on G2 and Spin(7)-manifolds},
author = {Jae-Hyouk Lee and Naichung Conan Leung},
journal= {arXiv preprint arXiv:math/0202045},
year = {2007}
}
Comments
Revised and updated version