Abstract
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 ω with respect to an orthonormal basis (Bilge et al. 1996a), is equivalent to the self-duality in the Hodge sense of ωn/2 (used in Grossman et al. 1984) and to the equality *ω = kωn−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.
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Özdemir, F., Bilge, A.H. Self-duality in dimensions 2n>4: equivalence of various definitions and the derivation of the octonionic instanton solution. ARI 51, 247–253 (1998). https://doi.org/10.1007/s007770050060
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DOI: https://doi.org/10.1007/s007770050060