We prove a nonexistence theorem for product-type manifolds. In particular, we show that the 4-manifold obtained from the product of closed surfaces does not admit any locally conformally flat metric arising from discrete and faithful representations for genus and .
"Locally conformally flat metrics on surfaces of general type." Illinois J. Math. 64 (1) 93 - 103, April 2020. https://doi.org/10.1215/00192082-8165606