  In the context of uniformisation problems, we study projective varieties with
klt singularities whose cotangent sheaf admits a projectively flat structure
over the smooth locus. Generalising work of Jahnke-Radloff, we show that torus
quotients are the only klt varieties with semistable cotangent sheaf and
extremal Chern classes. An analogous result for varieties with nef normalised
cotangent sheaves follows.
