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MiS Preprint
71/2006
The existence of symplectic 3-forms on 7-manifolds
Hông Vân Lê
Abstract
In this note we consider the existence problem for symplectic 3-forms on 7-manifolds. We find a first example of a closed 3-form of $\tilde G_2$-type on $S^3\times S^4$. We also prove that any integral symplectic 3-forms on a 7-manifold $M^7$ can be obtained by embedding $M^7$ to a universal space $( W^{N}, h)$, where $N = 3(81 + 8.C^3_8)$.
