A calibration form on a Riemannian manifold M is a differential p-form ϕ such that 1.ϕ is a closed form. 2. The comass of ϕ, sup_(v element ⋀^p T M, left bracketing bar v right bracketing bar = 1) left bracketing bar ϕ(v) right bracketing bar defined as the largest value of ϕ on a p vector of p-volume one, equals 1. A p-dimensional submanifold is calibrated when ϕ restricts to give the volume form.
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