The existence of symplectic 3-forms on 7-manifolds
نویسنده
چکیده
A k-form ω is called multi-symplectic, if Iω is a monomorphism. The classification (under the action ofGl(V )) of multi-symplectic 3-forms in dimension 7 has been done by Bures and Vanzura [B-V2002]. There are together 8 types of these forms, among them there two generic classes of G2-form ω 3 1 and G̃2-form ω 3 2 . They are generic in the sense of Gl(V )-action, more precisely the orbits Gl(V )(ω i ), i = 1, 2, are open sets in Λ (V ). The corresponding isotropy groups are the compact group G2 and its dual non-compact group G̃2. We shall write here a canonical expression of the G2-form ω 3 1 and G̃2-form ω 2 (see e.g. [Bryant1987], [B-V2002])
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