  Sets related to positively curved invariant Riemannian metrics on generalized
Wallach spaces are considered. The problem arises in studying of the evolution
of such metrics under the normalized Ricci flow equation. For Riemannian
metrics of the Wallach spaces $\operatorname{SU}(3)/T_{\max}$,
$\operatorname{Sp(3)}/ \left(\operatorname{Sp(1)}\right)^3$ and
$F_4/\operatorname{Spin(8)}$ which admit positive sectional curvature and
belong to a given invariant surface $\Sigma$ of the normalized Ricci flow we
established that they form a set bounded by three connected and pairwise
disjoint regular space curves such that each of them approaches two others
asymptotically at infinity. Analogously, for all generalized Wallach spaces the
set of Riemannian metrics which belong to $\Sigma$ and admit positive Ricci
curvature is bounded by three curves each consisting of two connected
components as regular curves. Intersections and asymptotical behaviors of these
components were studied as well.
