A calibrated manifold is a Riemannian manifold equipped with a closed differential p-form 
whose restriction to every oriented
tangent 
-plane
is at most its volume form. A submanifold on which equality holds is calibrated by
and is volume minimizing in its homology class.
Calibrated Manifold
See also
Differential k-Form, Riemannian Manifold, SubmanifoldExplore with Wolfram|Alpha
References
Harvey, R. and Lawson, H. B. Jr. "Calibrated Geometries." Acta Math. 148, 47-157, 1982.Cite this as:
Weisstein, Eric W. "Calibrated Manifold." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CalibratedManifold.html