A class of locally conformally flat 4-manifolds

Abstract

We construct infinite families of non-simply connected locally conformally flat (LCF) 4-manifolds realizing rich topological types. These manifolds have strictly negative scalar curvature and the underlying topological 4-manifolds do not admit any Einstein metrics. Such 4-manifolds are of particular interest as examples of Bach-flat but non-Einstein spaces in the non-simply connected case. Besides that the underlying smooth manifolds are examples of spaces that admit open book decomposition in dimension 4.

arXiv comment29 pages, 30 figures. Computation of the sign of the scalar curvature is improved. Title changed