Global behavior of the Ricci flow on homogeneous manifolds with two isotropy summands

TL;DR

This paper investigates the long-term evolution of the Ricci flow on specific homogeneous manifolds with two isotropy summands, revealing their global behavior and geometric transformations over time.

Contribution

It provides a comprehensive phase portrait analysis of Ricci flow on these manifolds, offering new insights into their geometric evolution.

Findings

Global phase portraits characterized

Geometrical consequences on manifold structure derived

Long-term behavior of Ricci flow elucidated

Abstract

In this paper we study the global behavior of the Ricci flow equation for two classes of homogeneous manifolds with two isotropy summands. Using methods of the qualitative theory of differential equations, we present the global phase portrait of such systems and derive some geometrical consequences on the structure of such manifolds under the action of the Ricci flow.