Parallel calibrations and minimal submanifolds
Given a parallel calibration φ ∈ Ωp(M) on a Riemannian manifold M, I prove that the φ-critical submanifolds with nonzero critical value are minimal submanifolds. I also show that the φ-critical submanifolds are precisely the integral manifolds of a C∞(M)-linear subspace P⊂Ωp(M). In particular, the calibrated submanifolds are necessarily integral submanifolds of the system. (Examples of parallel calibrations include the special Lagrangian calibration on Calabi-Yau manifolds, (co)associative calibrations on G2-manifolds, and the Cayley calibration on Spin(7)-manifolds.) © 2013 University of Illinois.
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