2000/10/05 by Nigel Hitchin, Hitchin, Nigel
Mathematics · Physics and Astronomy · #14J32 #53C25 #58E15 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th #math.AG #math.DG #msc:14J32 #msc:53C25 #msc:58E15
paper · pdf · doi:10.48550/arxiv.math/0010054
38 pages, LateX
arxiv created 2000/10/05 · arxiv updated 2009/11/30
We study the special algebraic properties of alternating 3-forms in 6 and 7 dimensions and introduce a diffeomorphism-invariant functional on the space of differential 3-forms on a closed manifold M in these dimensions. Restricting the functional to closed forms in a fixed cohomology class, we find that a critical point which is generic in a suitable sense defines in the 6-dimensional case a complex threefold with trivial canonical bundle and in 7 dimensions a Riemannian manifold with holonomy G2. This approach gives a direct method of finding a local moduli space, with its special geometry, for these structures.