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

Abstract

We present a unified eight-dimensional approach to instanton equations on several seven-dimensional manifolds associated to a six-dimensional homogeneous nearly Kahler manifold. The cone over the sine-cone on a nearly Kahler manifold has holonomy group Spin(7) and can be foliated by submanifolds with either holonomy group G(2), a nearly parallel G(2)-structure or a cocalibrated G(2)-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 R-7 and R-8 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.