Positive Ricci curvature on fiber bundles with compact structure group

TL;DR

This paper provides a straightforward proof for the existence of positive Ricci curvature metrics on fiber bundle total spaces with compact structure groups, generalizing previous results and constructing new examples including those with Ricci soliton bases.

Contribution

It offers a simple, direct proof for positive Ricci curvature on fiber bundles, extending prior work and unifying various results in the field.

Findings

Unified framework for positive Ricci curvature on fiber bundles

Construction of new manifolds with positive Ricci curvature

Application to bundles with Ricci soliton bases

Abstract

The aim of this paper is to present a direct and simple proof of a result concerning the existence of metrics of positive Ricci curvature on the total space of fiber bundles with compact structure groups. In particular, it also generalizes and puts in a unified framework the results in Nash \cite{nash} and Poor \cite{poor}. With the intention of disseminating this result, we apply it to build new examples of manifolds with positive Ricci curvature, including bundles whose base consists of gradient shrinking Ricci solitons.