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

2009/11/19 by Ricardo Miranda Martins, Lino Grama, Martins, Ricardo Miranda +1
Mathematics · Physics and Astronomy · #37C10 #37M99 #57M50 #57S25 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.0911.3781

openalex publication_date 2009/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• The Backward behavior of the Ricci and Cross Curvature Flows on SL(2,R)

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