Invariant metrics of positive Ricci curvature on principal bundles

Abstract.

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.