The conjecture on Sasakian-Einstein metrics for odd-dimensional spheres

An odd-dimensional sphere is the standard sphere $S^{2n+1}$, and a parallelizable manifold is a manifold with trivial tangent bundle. A Sasakian-Einstein metric is a Sasakian metric whose associated Riemannian metric is Einstein. The conjecture on odd-dimensional spheres. Every odd-dimensional sphere that bounds a parallelizable manifold admits a Sasakian-Einstein metric. The paper presents this as a conclusion suggested by the preceding constructions; no resolution is supplied in the source.