The existence of closed 3-forms of $\tilde G_2$-type on 7-manifolds
Abstract
Description
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.
10 pages, extended version of the first part of the previously submitted note. The second part of this note has been revised, extended and appeared in Archivum Math. 43 (2007) 443-457
10 pages, extended version of the first part of the previously submitted note. The second part of this note has been revised, extended and appeared in Archivum Math. 43 (2007) 443-457