Manifolds admitting a ${\tilde{G}}_2$-structure

Abstract

We find a necessary and sufficient condition for a compact 7-manifold to admit a ${\tilde{G}}_2$-structure. As a result we find a sufficient condition for an open 7-manifold to admit a closed 3-form of ${\tilde{G}}_2$-type.

4 pages, a new shorter exposition is given. the result has been included as Appendix in arXiv:1912.03338

References in corpus (1)

• Special metric structures and closed forms

Cited by in corpus (1)

• Multisymplectic 3-forms on 7-dimensional manifolds