The existence of closed 3-forms of ${\tilde{G}}_2$-type on 7-manifolds

Abstract

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

References in corpus (1)

• On the geometry of closed G2-structure