On metrics of positive Ricci curvature conformal to MxR^m

Details On metrics of positive Ricci curvature conformal to MxR^m On metrics of positive Ricci curvature conformal to MxR^m

2008-03-26

arxiv.org/abs/0803.3789v2

Mathematics

Differential Geometry

11 pages

Scientific paper

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

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