Bilge, Ayşe HümeyraBilge, Ayşe HümeyraDereli, TekinKoçak, Şahin2020-12-272020-12-27201701742-65881742-65961742-65881742-6596https://hdl.handle.net/20.500.12469/3690https://doi.org/10.1088/1742-6596/804/1/012005Let w be a 2-form on a 2n dimensional manifold. In previous work, we called w "strong self-dual, if the eigenvalues of its matrix with respect to an orthonormal frame are equal in absolute value. In a series of papers, we showed that strong self-duality agrees with previous definitions; in particular if w is strong self-dual, then, in 2n dimensions, w(n) is proportional to its Hodge dual w and in 4n dimensions, w(n) is Hodge self-dual. We also obtained a local expression of the Bonan 4-form on 8 manifolds with Spin7 holonomy, as the sum of the squares of any orthonormal basis of a maximal linear subspace of strong self-dual 2-forms. In the present work we generalize the notion of strong self-duality to odd dimensional manifolds and we express the dual of the Fundamental 3-form 7 manifolds with G(2) holonomy, as a sum of the squares of an orthonormal basis of a maximal linear subspace of strong self-dual 2-forms.eninfo:eu-repo/semantics/openAccessEquationsFieldsSpacesConference Object804WOS:00040404560000510.1088/1742-6596/804/1/0120052-s2.0-85017531606N/AN/A