Parallel calibrations and minimal submanifolds

Given a parallel calibration φ ∈ Ω^p(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⊂Ω^p(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.

Duke Scholars

Author Colleen M Robles Mathematics