Ricci Flow with hyperbolic warped product metrics

TL;DR

This paper demonstrates that negative curvature is maintained during Ricci flow of hyperbolic warped product metrics and that the flow ultimately converges to a flat metric over time.

Contribution

It establishes the preservation of negative curvature and convergence to flat metrics in Ricci flow for hyperbolic warped product geometries.

Findings

Negative curvature is preserved under Ricci flow.

The flow converges to a flat metric as time approaches infinity.

The result applies specifically to hyperbolic warped product metrics.

Abstract

In this short note, we show that the negative curvature is preserved in the deformation of hyperbolic warped product metrics under Ricci flow. It is also showed that the flow converges to a flat metric as time going to infinity.