A note on some classical results of Gromov-Lawson

TL;DR

This paper demonstrates how higher index theory can be used to extend classical non-existence results for complete Riemannian metrics with positive scalar curvature at infinity, showcasing the effectiveness of these methods.

Contribution

It improves classical results by Gromov and Lawson using higher index theory to establish non-existence theorems for certain Riemannian metrics.

Findings

Higher index theory proves non-existence of certain metrics

Improved classical results on scalar curvature

Method demonstrates effectiveness in geometric analysis

Abstract

In this short note we show how the higher index theory can be used to prove results concerning the non-existence of complete riemannian metric with uniformly positive scalar curvature at infinity. By improving some classical results due to M. Gromov and B. Lawson we show the efficiency of these methods in dealing with such non-existence theorems.