there are no conformal einstein rescalings of pseudo-riemannian einstein spaces with n complete light-like geodesics

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ID: 147211
2019
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Abstract
In the present paper, we study conformal mappings between a connected n-dimension pseudo-Riemannian Einstein manifolds. Let g be a pseudo-Riemannian Einstein metric of indefinite signature on a connected n-dimensional manifold M. Further assume that there is a point at which not all sectional curvatures are equal and through which in linearly independent directions pass n complete null (light-like) geodesics. If, for the function ψ the metric ψ − 2 g is also Einstein, then ψ is a constant, and conformal mapping is homothetic. Note that Kiosak and Matveev previously assumed that all light-lines were complete. If the Einstein manifold is closed, the completeness assumption can be omitted (the latter result is due to Mikeš and Kühnel).
Reference Key
mike2019mathematicsthere Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors ;Josef Mikeš;Irena Hinterleitner;Nadezda Guseva
Journal Turkish journal of pharmaceutical sciences
Year 2019
DOI
10.3390/math7090801
URL
https://www.mdpi.com/2227-7390/7/9/801
Keywords Keywords not found

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