Open Access
July, 2000 The Geometry of Three-Forms in Six Dimensions
Nigel Hitchin
J. Differential Geom. 55(3): 547-576 (July, 2000). DOI: 10.4310/jdg/1090341263


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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Nigel Hitchin. "The Geometry of Three-Forms in Six Dimensions." J. Differential Geom. 55 (3) 547 - 576, July, 2000.


Published: July, 2000
First available in Project Euclid: 20 July 2004

zbMATH: 1036.53042
MathSciNet: MR1863733
Digital Object Identifier: 10.4310/jdg/1090341263

Rights: Copyright © 2000 Lehigh University

Vol.55 • No. 3 • July, 2000
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