Ricci flow on certain homogeneous spaces

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 V 2 R n and V 1+k 2 R n , with n = 1 + k 2 + k 3 . We use techniques from the theory of differential equations, in particular the Poincaré compactification. This method allows us to study global phase portraits for polynomial differential systems.