Proceedings of the Japan Academy, Series A, Mathematical Sciences

Conformally flat metrics and $S^1$-fibration

Mitsuhiro Itoh, Naoko Nakada, and Takafumi Satou

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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

Permanent link to this document
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

Keywords
Conformally flat bundle metric $S^1$-bundle Yang-Mills connection

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


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References

  • M. Itoh, N. Nakada and T. Satou, $S^1$-Fibration and the conformal flatness, (2004). (In preparation).
  • M. Itoh, T. Satou, Circle bundle metric and the conformal flatness, (1998). (Preprint).
  • J. Lafontaine, Conformal geometry from the Riemannian viewpoint, in Conformal geometry (Bonn, 1985/1986), 65–92, Aspects Math. E12, Vieweg, Braunschweig 1998.
    Mathematical Reviews (MathSciNet): MR979789
    Digital Object Identifier: doi:10.1007/978-3-322-90616-8_3
  • T. Satou, Conformal flatness and self-duality of circle bundle metrics, Doctor thesis, Univ. of Tsukuba, (1998).
  • T. Satou, Conformal flatness of circle bundle metric, Tsukuba J. Math. 22 (1998), no. 2, 349–355.
    Mathematical Reviews (MathSciNet): MR1650741

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Proceedings of the Japan Academy, Series A, Mathematical Sciences

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