Characterization of conformally flat bundle metric on $S^1$-principal bundle is studied. It is shown further that there are infinitely many compact conformally flat $S^1$-principal bundles which are new examples, besides the Hopf fibration.
"Conformally flat metrics and $S^1$-fibration." Proc. Japan Acad. Ser. A Math. Sci. 81 (3) 61 - 63, March 2005. https://doi.org/10.3792/pjaa.81.61