Self-duality in higher dimensions

24th International Conference on Integrable Systems and Quantum symmetries

Bilge, A.H.^1 ; Dereli, T.^2 ; Kocak, S.^3

Kadir Has University, Turkey^1

Koç University, Turkey^2

Anadolu University, Turkey^3

关键词: Absolute values;    Eigenvalues;    Higher dimensions;    Linear subspace;    Local expression;    Orthonormal basis;    Orthonormal frames;    Self-duality;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/804/1/012005/pdf
DOI  :  10.1088/1742-6596/804/1/012005

来源: IOP

【 摘 要 】

Let ω be a 2-form on a 2n dimensional manifold. In previous work, we called ω "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 ω is strong self-dual, then, in 2n dimensions, ωnis proportional to its Hodge dual ω and in 4n dimensions, ωnis Hodge self-dual. We also obtained a local expression of the Bonan 4-form on 8 manifolds with Spin7holonomy, 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 G2holonomy, as a sum of the squares of an orthonormal basis of a maximal linear subspace of strong self-dual 2-forms.