## Proceedings of the Japan Academy, Series A, Mathematical Sciences

### Conformally flat metrics and $S^1$-fibration

#### Abstract

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.

#### Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 81, Number 3 (2005), 61-63.

Dates
First available in Project Euclid: 18 May 2005

https://projecteuclid.org/euclid.pja/1116442039

Digital Object Identifier
doi:10.3792/pjaa.81.61

Mathematical Reviews number (MathSciNet)
MR2128934

Zentralblatt MATH identifier
1114.53020

Subjects
Primary: 53A30: Conformal differential geometry

#### Citation

Itoh, Mitsuhiro; Nakada, Naoko; Satou, Takafumi. Conformally flat metrics and $S^1$-fibration. Proc. Japan Acad. Ser. A Math. Sci. 81 (2005), no. 3, 61--63. doi:10.3792/pjaa.81.61. https://projecteuclid.org/euclid.pja/1116442039

#### References

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• T. Satou, Conformal flatness of circle bundle metric, Tsukuba J. Math. 22 (1998), no. 2, 349–355.