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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 φ (for some 0 ≤ p ≤ n) which is a calibration, meaning that:φ is closed, that is, dφ = 0, where d is the exterior derivative.
φ has operator norm at most 1. That is, for any x ∈ M and any p-vector , we have φ(ξ) ≤ vol(ξ), with volume defined with respect to the Riemannian metric g.
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