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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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 $N = 3(81 + 8.C^3_8)$.

Received:
Aug 14, 2006
Published:
Aug 14, 2006
MSC Codes:
53C10, 53C42
Keywords:
symplectic 3-forms, $\tilde G_2$-forms, universal space

Related publications

Preprint
2006 Repository Open Access
Hông Vân Lê

The existence of symplectic 3-forms on 7-manifolds