2000/03/31 by Charles P. Boyer, Krzysztof Galicki
Mathematics · #math.DG #math.AG #msc:53C25 #msc:53C12 #msc:14E30
published as J. Diff. Geom. 57 (2001) 443-463. · Revised version with minor corrections and udated references, 15 pages, to appear in JDG
arxiv created 2001/09/05 · arxiv updated 2009/11/30
The purpose of this note is to introduce a new method for proving the existence of Sasakian-Einstein metrics on certain simply connected odd dimensional manifolds. We then apply this method to prove the existence of new Sasakian-Einstein metrics on \scriptstyleS2× S3 and on \scriptstyle(S2× S3)# (S2× S3). These give the first known examples of non-regular Sasakian-Einstein 5-manifolds. Our method involves describing the Sasakian-Einstein structures as links of certain isolated hypersurface singularities, and makes use of the recent work of Demailly and Kollár, AG/9910118, who obtained new examples of Kähler-Einstein del Pezzo surfaces with quotient singularities.