The Berger metric on a “squashed” three-sphere is given (in Euler coordinates) by 4 $ ds^2 = \lambda^2 (d \tau + \cos \theta d \phi)^2 + d \theta^2 + \sin^2 \theta d \phi^2$ . See for example Eq. 1.11 of this paper. This formula describes the geodesic distance between two infinitesimally separated points. My question:Read more