Journal of Differential Geometry

The Geometry of Three-Forms in Six Dimensions

Nigel Hitchin


We study the special algebraic properties of alternating 3-forms in 6 dimensions and introduce a diffeomorphism-invariant functional on the space of differential 3-forms on a closed 6-manifold M. Restricting the functional to a de Rham cohomology class in H3(M, R), we find that a critical point which is generic in a suitable sense defines a complex threefold with trivial canonical bundle. This approach gives a direct method of showing that an open set in H3(M, R) is a local moduli space for this structure and introduces in a natural way the special pseudo-Kähler structure on it.

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J. Differential Geom., Volume 55, Number 3 (2000), 547-576.

First available in Project Euclid: 20 July 2004

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Hitchin, Nigel. The Geometry of Three-Forms in Six Dimensions. J. Differential Geom. 55 (2000), no. 3, 547--576. doi:10.4310/jdg/1090341263.

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