Dirac flow on the 3-sphere
- Authors: Malkovich E.G.1
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Affiliations:
- Sobolev Institute of Mathematics
- Issue: Vol 57, No 2 (2016)
- Pages: 340-351
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/170402
- DOI: https://doi.org/10.1134/S0037446616020166
- ID: 170402
Cite item
Abstract
We illustrate some well-known facts about the evolution of the 3-sphere (S3, 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 S3 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.
About the authors
E. G. Malkovich
Sobolev Institute of Mathematics
Author for correspondence.
Email: malkovich@math.nsc.ru
Russian Federation, Novosibirsk