Conformal Fibrations of \(S^3\) by Circles

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Authors

  • Sebastian Heller

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Details

Original languageUndefined/Unknown
JournalContemp. Math.,
Publication statusPublished - 3 Dec 2013

Abstract

It is shown that analytic conformal submersions of \(S^3\) are given by intersections of (not necessary closed) complex surfaces with a quadratic real hyper-surface in \(\mathbb{C}P^3.\) A new description of the space of circles in the 3-sphere in terms of a natural bilinear form on the tangent sphere bundle of \(S^3\) is given. As an application it is shown that every conformal fibration of \(S^3\) by circles is the Hopf fibration up to conformal transformations.

Keywords

    math.DG, 35Q55, 53C42, 53A30

Cite this

Conformal Fibrations of \(S^3\) by Circles. / Heller, Sebastian.
In: Contemp. Math., 03.12.2013.

Research output: Contribution to journal › Article › Research › peer review

Heller, S 2013, 'Conformal Fibrations of \(S^3\) by Circles', Contemp. Math.,.
Heller, S. (2013). Conformal Fibrations of \(S^3\) by Circles. Contemp. Math.,.
Heller S. Conformal Fibrations of \(S^3\) by Circles. Contemp. Math.,. 2013 Dec 3.
Heller, Sebastian. / Conformal Fibrations of \(S^3\) by Circles. In: Contemp. Math.,. 2013.
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AB - It is shown that analytic conformal submersions of \(S^3\) are given by intersections of (not necessary closed) complex surfaces with a quadratic real hyper-surface in \(\mathbb{C}P^3.\) A new description of the space of circles in the 3-sphere in terms of a natural bilinear form on the tangent sphere bundle of \(S^3\) is given. As an application it is shown that every conformal fibration of \(S^3\) by circles is the Hopf fibration up to conformal transformations.

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