2001/02/22 by Charles P. Boyer, Krzysztof Galicki, Michael Nakamaye
Mathematics · #math.DG #msc:53C25 #msc:53C12 #msc:14E30
published as Transactions of the American Mathematical Society 354, 2983-2996 (2002) · 14 pages
arxiv created 2001/02/22 · arxiv updated 2009/11/30
We show that \scriptstyle#9(S2× S3) admits an 8-dimensional complex family of inequivalent non-regular Sasakian-Einstein structures. These are the first known Einstein metrics on this 5-manifold. In particular, the bound \scriptstyleb2(M)≤8 which holds for any regular Sasakian-Einstein \scriptstyleM does not apply to the non-regular case. We also discuss the failure of the Hitchin-Thorpe inequality in the case of 4-orbifolds and describe the orbifold version.