Positive Ricci curvature on fiber bundles with compact structure group

Abstract

The aim of this paper is to give a direct and simple proof and popularize a result for the existence of metrics of positive Ricci curvature on the total space of a large class of fiber bundles with compact structure groups. We use this result to build new examples of manifolds with positive Ricci curvature, including bundles which the basis consists on gradient shrinking Ricci solitons. In particular, it also generalizes and give an unified framework for the results in Nash [11] and Poor [12].