Einstein Metrics on Rational Homology 7-Spheres

2001/08/16 by Charles P. Boyer, Krzysztof Galicki, Michael Nakamaye
Mathematics · #math.DG #math.AG #msc:53C25 #msc:53C12 #msc:14E30

paper · pdf

published as Ann Inst. Fourier, 52 (2002), 1569-1584. · 19 pages

arxiv created 2001/08/16 · arxiv updated 2009/11/30

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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