Positive Ricci curvature on fiber bundles with compact structure group

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.

Exposition substantially improved. Examples added

References in corpus (4)

• Ricci flow with surgery on three-manifolds
• Examples of Riemannian Manifolds with non-negative sectional curvature
• Limiting behaviour of the Ricci flow
• On the geometry of some Equivariantly related manifolds

Cited by in corpus (1)

• The concept of Cheeger deformations on fiber bundles with compact structure group