Self-duality in dimensions 2n>4: equivalence of various definitions and the derivation of the octonionic instanton solution

摘要

We show that the notion of strong self-duality of 2-forms in dimensions 2n, defined by the equality of the absolute values of the eigenvalues of the matrix of #omega# with respect to an orthonormal basis (Bilge et al. 1996a), is equivalent to the self-duality in the Hodge sense of #omega# ~(n/2) (used in Grossman et al. 1984) and to the equality #omega# = k#omega#~(n-1)(used in Trautman 1977). We show that the octonionic instanton solution of Grossman et al. (1984), is uniquely determined from the minimality requirement of the second Pontrjagin number p_2