The conformal-Killing equation on G2 and Spin7 structures

Abstract

Let M be a 7-manifold with a G2-structure defined by \phi \in\Omega^{3}_{+}(M). We prove that {\phi} is conformal-Killing with respect to the associated metric g(\phi) if and only if the G2-structure is nearly parallel. Let M be an 8-manifold with a Spin7-structure defined by \psi \in\Omega^{4}_{+}(M). We prove that {\psi} is conformal-Killing with respect to the associated metric g(\psi) if and only if the Spin7-structure is parallel.