Parallel torsion and $$G_2, Spin(7)$$ instantons

Abstract Instanton properties of the characteristic connection $${\nabla }$$ ∇ on an integrable $$G_2$$ G 2 manifold as well as instanton condition of the torsion connection $${\nabla }$$ ∇ on a Spin (7) manifold are investigated. It is shown that for an integrable $$G_2$$ G 2 manifold with $${\nabla }$$ ∇ -parallel Lee form the curvature of the characteristic connection is a $$G_2$$ G 2 instanton exactly when the torsion 3-form is $${\nabla }$$ ∇ -parallel. It is observed that on a compact Spin (7) manifold with $${\nabla }$$ ∇ 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.