| Summary: | In the present paper, we study conformal mappings between a connected <i>n</i>-dimension pseudo-Riemannian Einstein manifolds. Let <i>g</i> be a pseudo-Riemannian Einstein metric of indefinite signature on a connected <i>n</i>-dimensional manifold <i>M</i>. Further assume that there is a point at which not all sectional curvatures are equal and through which in linearly independent directions pass <i>n</i> complete null (light-like) geodesics. If, for the function <inline-formula> <math display="inline"> <semantics> <mi>ψ</mi> </semantics> </math> </inline-formula> the metric <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>ψ</mi> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> <mi>g</mi> </mrow> </semantics> </math> </inline-formula> is also Einstein, then <inline-formula> <math display="inline"> <semantics> <mi>ψ</mi> </semantics> </math> </inline-formula> 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).
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