Topology and Geometry of Manifolds with Lower Curvature Bounds

Georgia Tech Research Corporation, Atlanta GA

Investigators

Abstract

ABSTRACT DMS - 0203979. This project deals with three areas of Riemannian geometry, namely, nonnegative sectional curvature, negative sectional curvature, and almost nonnegative Ricci curvature. Specifically, we continue the search of new examples of metrics of nonnegative sectional curvature and obstructions to their existence, especially in the simply-connected case, we plan to analyze the structure of open pinched negatively curved manifolds with nilpotent fundamental groups, and to study the difference between nonnegative and almost nonnegative Ricci curvatures. One of the main goals of modern geometry is to obtain global qualitative information about a space by measuring its local quantitative properties. Say, it has been known since the nineteenth century that a space that locally looks like an egg must globally look like an egg, not like a doughnut or a jungle gym. This project deals with similar matters for higher dimensional spaces, some of which occur naturally in physics and engineering.