of dimension n, to be denoted by Ric

interpolates between positive sectional and positive Ricci curvature

(when k=1 and k=n-1 respectively). It follows from the definition

that the smaller the k, the more restrictive the condition Ric

In this talk we will consider various kinds of metrics on closed

homogeneous spaces, and we will discuss how to estimate the

least k for which they satisfy Ric

various infinite families of manifolds (including generalized

Aloff-Wallach spaces) that are topologically distinct and admit

metrics of Ric

Miguel Dominguez-Vázquez and Lawrence Mouillé.