Homogeneous G2 and Sasakian instantons on the Stiefel 7-manifold

Abstract: We study homogeneous instantons on the seven dimensional Stiefel manifold V in the context of G2 and Sasakian geometry. According to the reductive decomposition of V we provide an explicit description of all invariant G2 and Sasakian structures. In particular, we characterise the invariant G2- structures inducing a Sasakian metric, among which the well known nearly parallel G2-structure (Sasaki- Einstein) is included. As a consequence, we classify the invariant connections on homogeneous principal bundles over V with gauge group U(1) and SO(3), satisfying either the G2 or the Sasakian instanton condition. Finally, we analyse the Yang Mills condition for those invariant connections.