An orbifold version of the Hitchin-Thorpe inequality is used to prove that certain weighted projective spaces do not admit orbifold Einstein metrics. Also, several estimates for the orbifold Yamabe invariants of weighted projective spaces are proved.
"Einstein metrics and Yamabe invariants of weighted projective spaces." Tohoku Math. J. (2) 65 (2) 297 - 311, 2013. https://doi.org/10.2748/tmj/1372182728