Locally conformally flat metrics on surfaces of general type

Abstract

We prove a nonexistence theorem for product type manifolds. In particular we show that the 4-manifold ${\Sigma }_g\times {\Sigma }_h$ does not admit any locally conformally flat metric arising from discrete and faithful representations for $g\ge 2$ and $h\ge 1$

Important typo in the statement of the main theorem is fixed. Section 3 is modified. 11 pages