Characterizations of subdual cones via isotonicity of the norm of the metric projection and via antitonicity of angular distance

Let $H$ be a real Hilbert space, let $K\subseteq H$ be a closed convex cone, let $K^*$ be its dual closed convex cone, and let $P_K$ denote the metric projection onto $K$. We study scalar quantities associated with th projection $P_K$ and their interaction with the preorder induced by $K$. Our main