Now showing items 1-2 of 2

  • Maximal linear subspaces of strong self-dual 2-forms and the Bonan 4-form 

    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. ...

  • Self-duality in higher dimensions 

    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 ...