Metrics of positive Ricci curvature on bundles

TL;DR

This paper constructs new examples of manifolds with positive Ricci curvature by analyzing vector bundles over manifolds with almost nonnegative Ricci curvature, expanding the known classes of such manifolds.

Contribution

It demonstrates that the total space of a vector bundle over a nonnegatively Ricci curved manifold, when producted with Euclidean space, admits a complete positive Ricci curvature metric.

Findings

E admits a positive Ricci curvature metric after product with R^p for large p

New examples of manifolds with positive Ricci curvature are constructed

Topological structures of these manifolds are vector bundles over almost nonnegative Ricci curvature manifolds

Abstract

We construct new examples of manifolds of positive Ricci curvature which, topologically, are vector bundles over compact manifolds of almost nonnegative Ricci curvature. In particular, we prove that if E is the total space of a vector bundle over a compact manifold of nonnegative Ricci curvature, then the product of E and R^p admits a complete metric of positive Ricci curvature for all large p.