Sasaki-Einstein Metrics on $S^2 \times S^3$

Abstract

In [9], Boyer and Galicki introduced a contact reduction method in the context of Sasakian manifolds, which produces 5-dimentional Sasaki-Einstein manifolds from a 7-sphere. In this paper, we compute very explicitly the metric obtained from the above mentioned reduction via a projection, $S^3 \times S^3 \to S^2 \times S^3$, and show that this metric is the homogeneous Kobayashi-Tanno metric.