 
Summary: Metrics of positive Ricci curvature on bundles
Igor Belegradek Guofang Wei \Lambda
May 11, 2001
Abstract
We construct new examples of manifolds of positive Ricci curvature which, topologi
cally, 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 E \Theta R p admits a complete metric of
positive Ricci curvature for all large p .
1 Introduction
According to the soul theorem of J. Cheeger and D. Gromoll, a complete open manifold of
nonnegative sectional curvature, denoted K – 0 , is the total space of a vector bundle over
a compact manifold with K – 0 . Manifolds of nonnegative Ricci curvature are much more
flexible, and nowadays there are many examples of complete manifolds of Ric – 0 which are
not even homotopy equivalent to complete manifolds of K – 0 . These include manifolds not
homotopy equivalent to closed manifolds [GM85], manifolds not satisfying Gromov's Betti
numbers estimate [SY89], manifolds of infinite topological type (see [Men00] and references
therein), manifolds with not virtuallyabelian fundamental group [Wei88], compact spin
Ricciflat 4manifolds with nonzero “
Agenus [Bes87, 6.27], [Lot00], and complements to
