Given a parallel $m$-calibration $\Omega$ on a Riemannian manifold $N$, we define for each $m$-submanifold $M$ an $\Omega$-angle that measures the deviation of $M$ to a $\Omega$-calibrated one. If $M$ is minimal but not $\Omega$-calibrated we expect that the $\Omega$-calibrated points can be expressed as a residue on a polinomial formula of invariants of $M$, the normal bundle $NM$, and $N$. This residue should be expressed on a PDE (possibly with singularities) on the $\Omega$-angle, via Chern-Weil theory. In this way, we propose to establish a link between two major theories of Harvey and Lawson: The theory of Calibrations and the one of Geometric Residues. We also propose the classification of minimal submanifolds with constant $\Omega$-angle. We study in detail the particular cases:

• Complex and Lagrangian points of Cayley 4-submanifolds of Calabi-Yau (real 8)-manifolds.
• Totally complex and quaternionic points of complex 4-submanifolds of Quaternionic-Kahler (QK) and Hyper-Kahler (HK) 8-manifolds.

Moreover, we give a description of complex submanifolds with constant quaternionic angle. We obtain some rigidity theorems for submanifolds of QK manifolds.