Abstract
A Sasaki-Einstein manifold is a Riemannian manifold (S, g) that is both Sasakian and Einstein. Sasakian geometry is the odd-dimensional cousin of Kahler geometry. Indeed, just as Kahler geometry is the natural intersection of complex, symplectic, and Riemannian geometry, so Sasakian geometry is the natural intersection of CR, contact, and Riemannian geometry. Perhaps the most straightforward definition is the following: a Riemannian manifold (S, g) is Sasakian if and only if its metric cone ( C(S) = R>0 × S, ḡ = dr 2 + r2g )
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