Positive scalar curvature and periodic fundamental groups

Abstract

is formed by double contraction of the riemannian curvature tensor of g (compare [He, pages 74-75]). Geometrically speaking, the scalar curvature function measures the difference between the volumes of the riemannian and euclidean geodesic disks. The existence of a riemannian metric with positive scalar curvature on a smooth manifold turns out to be of interest in many contexts. For example, by results of J. Kazdan and F. Warner [KW] the entire question of realizing a smooth function as a scalar curvature reduces to the existence of such a metric, and results of R. Schoen [Schn] on the Yamabe problem show that a metric with positive scalar curvature can be conformally deformed to one with