A class of locally conformally flat 4-manifolds

摘要

We construct infinite families of nonsimply connected locally conformally flat (LCF) 4-manifolds realizing rich topological types. These manifolds have strictly negativescalar curvature and the underlying topological 4-manifolds do notadmit any Einstein metrics. Such 4-manifolds are of particular interest as examples of Bach-flat but non-Einstein spaces in the nonsimply connected case.Besides that the underlying smooth manifolds are examples of spaces that admit open book decomposition in dimension 4.