The existence of closed 3-forms of $\tilde G_2$-type on 7-manifolds

Details The existence of closed 3-forms of $\tilde G_2$-type on 7-manifolds The existence of closed 3-forms of $\tilde G_2$-type on 7-manifolds

2006-03-08

arxiv.org/abs/math/0603182v5

Mathematics

Differential Geometry

10 pages, extended version of the first part of the previously submitted note. The second part of this note has been revised,

Scientific paper

In this note we construct a first example of a closed 3-form of $\tilde G_2$-type on $S^3\times S^4$. We prove that $S^3\times S^4$ does not admit a homogeneous 3-form of $\tilde G_2$-type. Thus our example is a first example of a closed 3-form of $\tilde G_2$-type on a compact 7-manifold which is not stably homogeneous.

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