Examples of complete manifolds with positive Ricci curvature

A long standing question in riemannian geometry has been: Does a complete manifold M n with positive Ricci curvature Ric also admit a complete metric with nonnegative sectional curvature K It is generally believed that this is not always true, but counterexamples were not known. The answer is actually affirmative for the dimension n = 3 (cf. [6], Note that K > 0 is sometimes known to be obstructed when a metric with Ric > 0 exists. Simple examples are S k X R' in the noncompact case