Asymptotically Euclidean metrics without conjugate points are flat

TL;DR

This paper proves that any asymptotically Euclidean metric on  space without conjugate points is necessarily flat, meaning it is isometric to the standard Euclidean metric.

Contribution

The paper establishes a rigidity result showing that such metrics must be flat, extending understanding of geometric structures without conjugate points.

Findings

Any asymptotically Euclidean metric without conjugate points is flat.

Such metrics are isometric to the Euclidean metric.

The result applies to  space, confirming flatness under these conditions.

Abstract

We prove that any asymptotically Euclidean metric on $\mathbb{R}^n$ with no conjugate points must be isometric to the Euclidean metric.