Yang-Mills instantons on cones and sine-cones over nearly Kähler manifolds

We present a unified eight-dimensional approach to instanton equations on several seven-dimensional manifolds associated to a six-dimensional homogeneous nearly Kähler manifold. The cone over the sine-cone on a nearly Kähler manifold has holonomy group Spin(7) and can be foliated by submanifolds with either holonomy group G₂, a nearly parallel G₂-structure or a cocalibrated G₂-structure. We show that there is a G ₂-instanton on each of these seven-dimensional manifolds which gives rise to a Spin(7)-instanton in eight dimensions. The well-known octonionic instantons on R⁷ and R⁸ are contained in our construction as the special cases of an instanton on the cone and on the cone over the sine-cone, both over the six-sphere, respectively.