Einstein Metrics on Exotic Spheres in Dimensions 7, 11, and 15

Details Einstein Metrics on Exotic Spheres in Dimensions 7, 11, and 15 Einstein Metrics on Exotic Spheres in Dimensions 7, 11, and 15

2003-11-17

arxiv.org/abs/math/0311293v1

Experimental Mathematics 14 (2005), 61-66.

Mathematics

Differential Geometry

7 pages

Scientific paper

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 \cite{BGK}, 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 8610 deformation classes of Sasakian-Einstein metrics into the 28 distinct oriented diffomorphism types in dimension $7.$

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