Compact Complex Surfaces of Locally Conformally Flat Type

Abstract

We show that if a compact complex surface admits a locally conformally flat metric, then it cannot contain a smooth rational curve of odd self-intersection. In particular, the surface has to be minimal. Then we give a list of possibilities of such surfaces.

14 pages, Final version with journal information

References in corpus (1)

• Locally conformally flat and self-dual structures on simple 4-manifolds