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The geometry of three-forms in six dimensions. (English) Zbl 1036.53042
In this paper the author studies special algebraic properties of alternating 3-forms in six dimensions and introduces 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 \(H^3(M,{\mathbb R})\), he finds 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 \(H^3(M,{\mathbb R})\) is a local moduli space for this structure and introduces in a natural way the special pseudo-Kähler structure on it.

53C43 Differential geometric aspects of harmonic maps
53C55 Global differential geometry of Hermitian and Kählerian manifolds
58D27 Moduli problems for differential geometric structures
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