Conformal deformation on a semi-Riemannian manifold. I (Q2732147)
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scientific article; zbMATH DE number 1623262
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Conformal deformation on a semi-Riemannian manifold. I |
scientific article; zbMATH DE number 1623262 |
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4 September 2002
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Lorentzian geometry
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warped product
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conformal transformation
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scalar curvature
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Conformal deformation on a semi-Riemannian manifold. I (English)
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The paper studies Lorentzian manifolds of arbitrary dimension endowed with a warped product metric \(g=-dt^2+ f(t)^2g_0\) and with scalar curvature \(+1\). It is shown that under mild conditions on \(f(t)\) a conformal transformation \(g\mapsto \varphi(t)g\) maps to a manifold of the same type only if \(\varphi(t) \equiv 1\). Additionally, a result on more general conformal transformations is presented.
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