Arithmetic manifolds of positive scalar curvature

Arithmetic Manifolds of Positive Scalar Curvature

Simply Connected Manifolds of Positive Scalar Curvature

Hitchin proved that if M is a spin manifold with positive scalar curvature, then the A^O-characteristic number a(M) vanishes. Gromov and Lawson conjectured that for a simply connected spin manifold M of dimension > 5, the vanishing of a(M) is sufficient for the existence of a Riemannian metric on M with positive scalar curvature. We prove this conjecture using techniques from stable homotopy th...

Positive Scalar Curvature of Totally Nonspin Manifolds

In this paper we address the issue of positive scalar curvature on oriented nonspin compact manifolds whose universal cover is also nonspin. We provide a conjecture for an obstruction to such curvature in this venue that takes into account all the data known to date. The conjecture is proved for a wide class of closed manifolds based on their fundamental group structure.

Curvature Estimates in Asymptotically Flat Manifolds of Positive Scalar Curvature

Suppose that (Mn, g) is an asymptotically flat Riemannian spin manifold of positive scalar curvature. The positive mass theorem [1, 2, 3] states that the total mass of the manifold is always positive, and is zero if and only if the manifold is flat. This result suggests that there should be an inequality which bounds the Riemann tensor in terms of the total mass and implies that curvature must ...

Curvature Estimates in Asymptotically At Manifolds of Positive Scalar Curvature