New York Journal of Mathematics
Volume 18 (2012) 733-763


Selman Akbulut and Mustafa Kalafat

A class of locally conformally flat 4-manifolds

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Published: October 6, 2012
Keywords: Locally conformally flat metrics, Kleinian groups, scalar curvature, handlebody theory
Subject: 58D27, 58A05, 57R65

We construct infinite families of nonsimply 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 nonsimply connected case. Besides that the underlying smooth manifolds are examples of spaces that admit open book decomposition in dimension 4.


The first named author is partially supported by NSF grant DMS 9971440

Author information

Selman Akbulut:
Mathematics Department, Michigan State University, East Lansing, MI 48824

Mustafa Kalafat:
Mathematics Department, University of Wisconsin at Madison
Current Address: Tunceli \" Universitesi, Bilgisayar M\" uhendisli\v gi B\" ol\" um\" u, Turkia.