Conformally flat metrics and \(S^1\)-fibration. (English) Zbl 1114.53020

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.


53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
53C20 Global Riemannian geometry, including pinching
Full Text: DOI Euclid


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