High Quality Content by WIKIPEDIA articles! In the mathematical field of differential geometry, a calibrated manifold is a Riemannian manifold (M,g) of dimension n equipped with a differential p-form ? (for some 0 ? p ? n) which is a calibration in the sense that * ? is closed: d? = 0, where d is the exterior derivative * for any x ? M and any oriented p-dimensional subspace ? of TxM, ?|? = ? vol? with ? ? 1. Here vol? is the volume form of ? with respect to g. Set Gx(?) = { ? as above : ?|? = vol? }. (In order for the theory to be nontrivial, we need Gx(?) to be nonempty.) Let G(?) be the union of Gx(?) for x in M. The theory of calibrations is due to R. Harvey and B. Lawson and others (see The History of Calibrations).

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