Parallel torsion and G₂, Spin (7) instantons

Instanton properties of the characteristic connection on an integrable G₂ manifold as well as instanton condition of the torsion connection on a Spin (7) manifold are investigated. It is shown that for an integrable G₂ manifold with -parallel Lee form the curvature of the characteristic connection is a G₂ instanton exactly when the torsion 3-form is -parallel. It is observed that on a compact Spin (7) manifold with closed torsion 3-form the torsion connection is a Spin (7) instanton if and only if the torsion 3-form is parallel with respect to the torsion connection.