Sasaki-Einstein metrics on \(S^2 \times S^3\) (Q1943242)

\textit{S. Tanno} in [Minimal submanifolds and geodesics, Proc. Jap.-U.S. Semin., Tokyo 1977, 283--292 (1979; Zbl 0441.53038)] showed that the unit tangent bundle of a unit \(m\)-sphere admits an Einstein metric which is homogeneous and irreducible; in particular \(S^2\times S^3\) admits an Einstein metric which is not a Riemannian product. In the present paper the author gives a very explicit expression for this metric in terms of local coordinates on \(S^2\times S^3\). The technique to produce this expression stems from the idea of Sasakian reduction from the 7-sphere as introduced in [\textit{C. P. Boyer} and \textit{K. Galicki}, Sasakian geometry. Oxford: Oxford University Press (2008; Zbl 1155.53002)].