The dynamical Alekseevskii conjecture in dimension five

2025/07/23 by Maher Billon, Billon, Maher
Computer Science · Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2507.17781

openalex publication_date 2025/07/23 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

We prove the dynamical Alekseevski conjecture in dimension five. We also provide a detailed analysis of the homogeneous Ricci flows on SO(3)\ltimes ℝ³/SO(2) and SL(2,ℂ)/U(1).

Citations

• The Alekseevskii conjecture in low dimensions
• Scalar curvature behavior of homogeneous Ricci flows
• Ricci flow of homogeneous manifolds

Related

• Homogeneous Ricci solitons in low dimensions
• Long-time behavior of awesome homogeneous Ricci flows
• Ricci flow on locally homogeneous closed 4-manifolds
• Ricci Flow of Compact Locally Homogeneous Geometries on 5-Manifolds
• The Alekseevskii conjecture in low dimensions