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Dirac flow on the 3-sphere

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Abstract

We illustrate some well-known facts about the evolution of the 3-sphere (S 3, g) generated by the Ricci flow. We define the Dirac flow and study the properties of the metric \(\bar g = dt^2 + g(t)\), where g(t) is a solution of the Dirac flow. In the case of a metric g conformally equivalent to the round metric on S 3 the metric \(\bar g\) is of constant curvature. We study the properties of solutions in the case when g depends on two functional parameters. The flow on differential 1-forms whose solution generates the Eguchi–Hanson metric was written down. In particular cases we study the singularities developed by these flows.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    E. G. Malkovich

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  1. E. G. Malkovich
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Correspondence to E. G. Malkovich.

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The author was supported by the Government of the Russian Federation (Grant 14.B25.31.0029).

Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 57, No. 2, pp. 432–446, March–April, 2016; DOI: 10.17377/smzh.2016.57.216.

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Malkovich, E.G. Dirac flow on the 3-sphere. Sib Math J 57, 340–351 (2016). https://doi.org/10.1134/S0037446616020166

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  • DOI: https://doi.org/10.1134/S0037446616020166

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