Calibrations and spinors
type: Item
instance of: scholarly article
title: Calibrations and spinors
zbMATH Open document ID: 0782.53029
DOI: 10.1007/BF02392455
author: Jiri Dadok
author: F. Reese Harvey
published in: Acta Mathematica
publication date: 1994-03-07T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 205189
zbMATH Keywords: integral submanifolds
reviewed by: James Hebda
MaRDI profile type: Publication
cites work: Polar Coordinates Induced by Actions of Compact Lie Groups
cites work: Q3996563
cites work: Calibrated geometries
cites work: Q3897665
description: scientific article; zbMATH DE number 205189