The space of nonpositively curved metrics of a negatively curved manifold

TL;DR

This paper investigates the structure of the space of nonpositively curved metrics on negatively curved manifolds, revealing that this space is highly disconnected, which has implications for geometric topology.

Contribution

It demonstrates that the space of nonpositively curved metrics on a negatively curved manifold is highly non-connected, a novel insight into the geometric structure of such metrics.

Findings

The space of nonpositively curved metrics is highly disconnected.

Negatively curved manifolds admit a complex space of nonpositively curved metrics.

The topology of the metric space impacts geometric and topological properties.

Abstract

We show that the space of nonpositively curved metrics of a negatively curved manifold is highly non connected.