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On metrics of positive Ricci curvature conformal to M × 𝐑 m

Juan Miguel Ruiz — 2009

Archivum Mathematicum

Let ( M n , g ) be a closed Riemannian manifold and g E the Euclidean metric. We show that for m > 1 , M n × 𝐑 m , ( g + g E ) is not conformal to a positive Einstein manifold. Moreover, M n × 𝐑 m , ( g + g E ) is not conformal to a Riemannian manifold of positive Ricci curvature, through a radial, integrable, smooth function, ϕ : 𝐑 𝐦 𝐑 + , for m > 1 . These results are motivated by some recent questions on Yamabe constants.

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