Calibrations and spinors
The second author and \textit{H. B. Lawson jun.} [ibid. 148, 47-157 (1982; Zbl 0584.53021)] inaugurated the study of calibrations and explained their importance to differential geometry. In the paper under review, a general procedure is described for constructing calibrations with constant coefficients on \(R^{8m}\) by squaring spinors. This procedure is analyzed in detail in dimension 16. Explicit calculations of new calibrations on \(R^{16}\) are presented. In addition, they prove that in general, the submanifolds calibrated by the calibrations constructed by this procedure are integral submanifolds for some differential system. Also, since constant coefficient calibrations on \(R^ p\) can be used to construct calibrations on \(R^{p-1}\), they are able to analyze the family of calibrations on \(R^{15}\) that come from squaring spinors.
scientific article; zbMATH DE number 205189