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2005 Einstein Metrics on Exotic Spheres in Dimensions 7, 11, and 15
Charles P. Boyer, Krzysztof Galicki, János Kollár, Evan Thomas
Experiment. Math. 14(1): 59-64 (2005).


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.


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Charles P. Boyer. Krzysztof Galicki. János Kollár. Evan Thomas. "Einstein Metrics on Exotic Spheres in Dimensions 7, 11, and 15." Experiment. Math. 14 (1) 59 - 64, 2005.


Published: 2005
First available in Project Euclid: 30 June 2005

zbMATH: 1112.53033
MathSciNet: MR2146519

Primary: 53C25

Keywords: Einstein metrics , exotic spheres , Kähler-Einstein orbifolds , Sasakian manifolds

Rights: Copyright © 2005 A K Peters, Ltd.


Vol.14 • No. 1 • 2005
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