Two remarks on $PQ^{\epsilon}$-projectivity of Riemannian metrics
  We show that $PQ^{\epsilon}$-projectivity of two Riemannian metrics introduced in \cite{Top2003} implies affine equivalence of the metrics unless $\epsilon\in\{0,-1,-3,-5,-7,...\}$. Moreover, we show that for $\epsilon=0$, $PQ^{\epsilon}$-projectivity implies projective equivalence. 
Vladimir S. Matveev, Stefan Rosemann
math.DG