2023/07/12 by Leonardo F. Cavenaghi, Lino Grama, Cavenaghi, Leonardo F. +5
Mathematics · Physics and Astronomy · #14M15 #37C20 #53C23 #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.2307.06418
openalex publication_date 2023/07/12 · openalex created_date 2023/07/15 · openalex updated_date 2026/08/01
The family of invariant Riemannian manifolds in the Wallach flag manifold SU(3)/T2 is described by three parameters (x,y,z) of positive real numbers. By restricting such a family of metrics in the tetrahedron \calT:= x+y+z = 1, in this paper, we describe all regions \cal R ⊂ \cal T admitting metrics with curvature properties varying from positive sectional curvature to positive scalar curvature, including positive intermediate curvature notion's. We study the dynamics of such regions under the projected Ricci flow in the plane (x,y), concluding sign curvature maintenance and escaping. In addition, we obtain some results for positive intermediate Ricci curvature for a path of metrics on fiber bundles over SU(3)/T2, further studying its evolution under the Ricci flow on the base.