We prove that a vacuum static space admitting a non-trivial gradient conformal vector field is isometric to a Euclidean space or to a warped product $\mathrm{I}\times_\varphi\mathfrak{L}^{m-1}$ of an interval $\mathrm{I}$ and an Einstein manifold $\mathfrak{L}^{m-1}$, provided that scalar curvature of $\mathfrak{L}^{m-1}$ is constant.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:The purpose of this work is to study the conformal geometry of vacuum static spaces with a constant scalar curvature, which corresponds to an interesting generalization of the critical point of the equation.
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Temel Bulgular & Veri:The purpose of this work is to study the conformal geometry of vacuum static spaces with a constant scalar curvature, which corresponds to an interesting generalization of the critical point of the equation.
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Sonuç & Katkı:We prove that a vacuum static space admitting a non-trivial gradient conformal vector field is isometric to a Euclidean space or to a warped product $\mathrm{I}\times_\varphi\mathfrak{L}^{m-1}$ of an interval $\mathrm{I}$ and an Einstein manifold $\mathfrak{L}^{m-1}$, provided that scalar curvature of $\mathfrak{L}^{m-1}$ is constant.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:vacuum static spaces · closed conformal vector field · gradient conformal vector field
Abstract
The purpose of this work is to study the conformal geometry of vacuum static spaces with a constant scalar curvature, which corresponds to an interesting generalization of the critical point of the equation. We prove that a vacuum static space admitting a non-trivial gradient conformal vector field is isometric to a Euclidean space or to a warped product $\mathrm{I}\times_\varphi\mathfrak{L}^{m-1}$ of an interval $\mathrm{I}$ and an Einstein manifold $\mathfrak{L}^{m-1}$, provided that scalar curvature of $\mathfrak{L}^{m-1}$ is constant.
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