The curvature operator at the soul

TL;DR

This paper proves two splitting theorems for open manifolds with nonnegative sectional curvature, one topological and one metric, advancing understanding of their geometric and topological structure.

Contribution

It introduces new splitting theorems specifically for open manifolds with nonnegative sectional curvature, enriching the theoretical framework.

Findings

Proves a topological splitting theorem.

Establishes a metric splitting theorem.

Abstract

We prove two splitting theorems, one topological, the other metric, for open manifolds with nonnegative sectional curvature.