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A Sasakian manifold is a contact manifold $(M,\theta)$ equipped with a special kind of Riemannian metric $g$, called a Sasakian metric.
3
votes
Paper about Sasaki-Einstein manifolds
I agree with Spiro's recommendation to pick up the book by Boyer and Galicki, but I would like to add the following.
There are at least two ways to get to Sasaki-Einstein manifolds. The traditional a …
3
votes
Accepted
Is every 3-Sasakian a Sasakian-Einstein manifold?
Yes, because a manifold is Sasaki-Einstein if and only if its metric cone is Ricci-flat Kähler, whereas the cone of a 3-sasakian manifold is hyperkähler.
See, for instance, Bär's "Real Killing spinors …