Invariant metrics of positive Ricci curvature on principal bundles
Let \(Y\) be a compact connected Riemannian manifold with a metric of positive Ricci curvature. Let \(\pi:P\rightarrow Y\) be a principal bundle over \(Y\) with compact connected structure group \(G\). If the fundamental group of \(P\) is finite, we show that \(P\) admits a \(G\) invariant metric with positive Ricci curvature so that \(\pi\) is a Riemannian submersion.
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