Ricci flow on certain homogeneous spaces

2020/02/26 by Statha, Marina
#34A26 #53C25 #53C30 #53E20 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2002.12175

Abstract

We study the behavior of the normalized Ricci flow of invariant Riemannian homogeneous metrics at infinity for generalized Wallach spaces, generalized flag manifolds with four isotropy summands and second Betti number equal to one, and the Stiefel manifolds V₂ℝⁿ and V_1+k2ℝⁿ, with n = 1+k₂+k₃. We use techniques from the theory of differential equations, in particular the Poincaré compactification.

Related

• Ricci flow of homogeneous manifolds
• Refined behavior description of the normalized Ricci flow on homogeneous spaces
• Ricci flow on homogeneous spaces with two isotropy summands
• The projected homogeneous Ricci flow and three-isotropy-summands flag manifolds
• The Ricci curvature and the normalized Ricci flow on the Stiefel manifolds SO(n)/SO(n-2)