Sasaki-Einstein metrics on S2 × S3

Abstract

In, 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, S3 × S3 → S2 × S3, and show that this metric is the homogeneous Kobayashi-Tanno metric.