Dirac flow on the 3-sphere
type: Item
instance of: scholarly article
title: Dirac flow on the 3-sphere
zbMATH Open document ID: 1351.53082
DOI: 10.1134/S0037446616020166
author: E. G. Malkovich
published in: Siberian Mathematical Journal
publication date: 2016-07-29T00:00:00Z
review text: The author defines and studies the Dirac flow: \({\frac {\partial g}{\partial t}=\sqrt{\mathrm{Ric}(g)-4Kg}}\), where \(g\) is a metric conformally equivalent to the round metric on the sphere \(S^3\); this flow describes metrics of constant curvature. Also this flow is studied in the case when \(g(t)\) depends on two functional parameters. Moreover the flow on \(\mathbb{R}P^3\) which gives the Eguchi-Hanson metric is defined by \({\frac {{\partial g}_{ij}}{\partial t}}={1\over 2}{\sqrt{\det(\mathrm{Ric})}({\mathrm{Ric}^{-1})_{ij}}}\), where \(i,j \in \{1,2,3\}\). Finally, singularities developed by these flows are studied in some cases.
reviewed by: Antonella Nannicini
Mathematics Subject Classification ID: 53C44
Mathematics Subject Classification ID: 35Q41
zbMATH DE Number: 6607750
zbMATH Keywords: Dirac flow
zbMATH Keywords: Ricci flow
zbMATH Keywords: spaces of constant curvature
zbMATH Keywords: Eguchi-Hanson metric
zbMATH Keywords: Hitchin flow
MaRDI profile type: Publication
cites work: Ricci Flow on 3-dimensional Lie groups and 4-dimensional Ricci-flat manifolds
cites work: Q5731354
cites work: Einstein manifolds
cites work: Self-dual solutions to Euclidean gravity
cites work: Q3597177
cites work: Spin(7)-structures on complex linear bundles and explicit Riemannian metrics with holonomy group SU(4)
cites work: On the new examples of complete noncompact Spin(7)-holonomy metrics
full work available at URL: s0037446616020166
OpenAlex ID: W2400293371
Wikidata QID: Q126213886
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description: scientific article; zbMATH DE number 6607750