QR-submanifolds and Riemannian metrics with $G_2$ holonomy
  In this note we prove that QR-submanifolds of the hyper-Kahler manifolds under some conditions admit the $G_2$ holonomy. We give simplest examples of such QR-submanifolds namely tori.   We conjecture that all $G_2$ holonomy manifolds arise in this way. 
Dmitry Egorov
math.DG