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.