The geometry of three-forms in six and seven dimensions

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dc.creatorHitchin, Nigel
dc.date2000-10-05
dc.date.accessioned2026-07-07T04:37:51Z
dc.date.available2026-07-07T04:37:51Z
dc.descriptionWe 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.
dc.description38 pages, LateX
dc.identifierhttps://arxiv.org/abs/math/0010054
dc.identifierhttp://arxiv.org/abs/math/0010054
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60061
dc.subjectDifferential Geometry
dc.subjectHigh Energy Physics - Theory
dc.subjectAlgebraic Geometry
dc.subject14J32; 53C25; 58E15
dc.titleThe geometry of three-forms in six and seven dimensions
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