Einstein Metrics on Rational Homology 7-Spheres
Charles P. Boyer, Krzysztof Galicki, Michael Nakamaye
Abstract
In this paper we demonstrate the existence of Sasakian-Einstein structures on certain 2-connected rational homology 7-spheres. These appear to be the first non-regular examples of Sasakian-Einstein metrics on simply connected rational homology spheres. We also briefly describe the rational homology 7-spheres that admit regular positive Sasakian structures.
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