Before revision:  The key idea is to compute the projection with respect to the norm defined by the low-rank approximation . Hence, PNKH-B can be viewed as a projected variable metric method.
After revision:  The key idea is to compute the projection with respect to the norm defined by the low-rank approximation of the Hessian on the Krylov subspace. This renders PNKH-B can be viewed as a projected variable metric method.