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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.

MSC:

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

[1] M. Itoh, N. Nakada and T. Satou, \(S^1\)-Fibration and the conformal flatness, (2004). (In preparation). · Zbl 1114.53020
[2] M. Itoh, T. Satou, Circle bundle metric and the conformal flatness, (1998). (Preprint). · Zbl 0977.53509
[3] J. Lafontaine, Conformal geometry from the Riemannian viewpoint, in Conformal geometry ( Bonn, 1985/1986 ), 65-92, Aspects Math. E12, Vieweg, Braunschweig 1998. · Zbl 0661.53008 · doi:10.1007/978-3-322-90616-8_3
[4] T. Satou, Conformal flatness and self-duality of circle bundle metrics, Doctor thesis, Univ. of Tsukuba, (1998). · Zbl 0977.53509
[5] T. Satou, Conformal flatness of circle bundle metric, Tsukuba J. Math. 22 (1998), no. 2, 349-355. · Zbl 0977.53509
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