Refined behavior description of the normalized Ricci flow on homogeneous spaces

2025/08/10 by Nurlan Abiev, Abiev, Nurlan A.
Mathematics · Physics and Astronomy · #34C05 #37C10 #53C30 #53E20 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2508.07391

openalex publication_date 2025/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article deals with the problems of preserving the Ricci curvature positivity on homogeneous spaces under the normalized Ricci flow (NRF). We found out infinitely many generalized Wallach spaces (GWS) on which the positivity of the Ricci curvature of metrics is preserved when evolved by the NRF. Analogously, the number of GWS is infinite as well, when the positivity of the Ricci curvature can be lost. We also obtain some refinements to our previous results devoted to the case of coincided parameters. A series of examples is discussed.

Citations

• Ricci curvature and normalized Ricci flow on generalized Wallach spaces
• On the dynamics of a three-dimensional differential system related to the normalized Ricci flow on generalized Wallach spaces
• On the dynamics of positively curved metrics on SU(3)/T² under the homogeneous Ricci flow
• Positive intermediate curvatures and Ricci flow

Related

• Ricci curvature and normalized Ricci flow on generalized Wallach spaces
• Ricci flow on certain homogeneous spaces
• On the dynamics of a three-dimensional differential system related to the normalized Ricci flow on generalized Wallach spaces
• On the dynamics of positively curved metrics on SU(3)/T² under the homogeneous Ricci flow
• On properties of the sets of positively curved Riemannian metrics on generalized Wallach spaces