Refined behavior description of the normalized Ricci flow on homogeneous spaces

Abstract: This article deals with the problems of preserving the Ricci curvature positivity on homogeneous spaces under the normalized Ricci flow (NRF). We found out infinitely many generalized Wallach spaces (GWS) on which the positivity of the Ricci curvature of metrics is preserved when evolved by the NRF. Analogously, the number of GWS is infinite as well, when the positivity of the Ricci curvature can be lost. We also obtain some refinements to our previous results devoted to the case of coincided parameters. A series of examples is discussed.