Browsing by Author "Dereli, Tekin"

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Citation Count: 2
Maximal linear subspaces of strong self-dual 2-forms and the Bonan 4-form
(Elsevier Science Inc, 2011) Bilge, Ayşe Hümeyra; Dereli, Tekin; Koçak, Şahin
The notion of self-duality of 2-forms in 4-dimensions plays an eminent role in many areas of mathematics and physics, but although the 2-forms have a genuine meaning related to curvature and gauge-field-strength in higher dimensions also, their "self-duality" is something which is almost avoided above 4-dimensions. We show that self-duality of 2-forms is a very natural notion in higher (even) dimensions also and we prove the equivalence of some scattered and rarely used definitions in the literature. We demonstrate the usefulness of this higher self-duality by studying it in 8-dimensions and we derive a natural expression for the Bonan form in terms of self-dual 2-forms and we give an explicit expression of the local action of SO(8) on the Bonan form. (C) 2010 Elsevier Inc. All rights reserved.
Citation Count: 0
Self-duality in higher dimensions
(IOP Publishing Ltd, 2017) Bilge, Ayşe Hümeyra; Dereli, Tekin; Koçak, Şahin
Let 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.