Einstein Metrics on Exotic Spheres in Dimensions 7, 11, and 15
Boyer, Charles P. ; Galicki, Krzysztof ; Kollár, János ; Thomas, Evan
Experiment. Math., Tome 14 (2005) no. 1, p. 59-64 / Harvested from Project Euclid
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In a recent article the first three authors proved that in dimension $4m+1$ all homotopy spheres that bound parallelizable manifolds admit Einstein metrics of positive scalar curvature which, in fact, are Sasakian-Einstein. They also conjectured that all such homotopy spheres in dimension $4m-1, m\geq2$ admit Sasakian-Einstein metrics, and proved this for the simplest case, namely dimension 7. In this paper we describe computer programs that show that this conjecture is also true for 11-spheres and 15-spheres. Moreover, a program is given that determines the partition of the 8,610 deformation classes of Sasakian-Einstein metrics into the 28 distinct oriented diffomorphism types in dimension 7.
Publié le : 2005-05-14
Classification:  Einstein metrics,  Sasakian manifolds,  exotic spheres,  Kähler-Einstein orbifolds,  53C25 
@article{1120145570,
     author = {Boyer, Charles P. and Galicki, Krzysztof and Koll\'ar, J\'anos and Thomas, Evan},
     title = {Einstein Metrics on Exotic Spheres in Dimensions 7, 11, and 15},
     journal = {Experiment. Math.},
     volume = {14},
     number = {1},
     year = {2005},
     pages = { 59-64},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1120145570}
}

Boyer, Charles P.; Galicki, Krzysztof; Kollár, János; Thomas, Evan. Einstein Metrics on Exotic Spheres in Dimensions 7, 11, and 15. Experiment. Math., Tome 14 (2005) no. 1, pp.  59-64. http://gdmltest.u-ga.fr/item/1120145570/