Ricci curvature and volume growth

Martin Strake and Gerard Walschap

Vol. 148 (1991), No. 1, 161–167

DOI: 10.2140/pjm.1991.148.161

Abstract

We give an example of a complete manifold M^m of nonnegative Ricci curvature for which the volume of distance tubes around a totally geodesic submanifold L¹ divided by the corresponding volume in L × R^m−1 goes to infinity. Recall that in the case of nonnegative sectional curvature, this quotient is nonincreasing and bounded by 1.

Mathematical Subject Classification 2000

Primary: 53C21

Secondary: 53C20

Milestones

Received: 29 September 1989

Published: 1 March 1991