Abstract
We prove that energy minimizing Yang–Mills connections on a compact G 2 -manifold has holonomy equal to G 2 are G 2 -instantons, subject to an extra condition on the curvature. Furthermore, we show that energy minimizing connections on a compact Calabi–Yau 3 -fold that has holonomy equal to S U ( 3 ) subject to a similar condition are holomorphic.
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