Sasaki-Einstein Metrics on S 2 × S 3

. 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 × S 3 → S 2 × S 3 , and show that this metric is the homogeneous Kobayashi-Tanno metric.