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Recently, we have studied evolution of a family of Finsler metrics alongFinsler Ricci flow and proved its convergence in short time. Here, evolutionequation of the reduced $hh$-curvature and the Ricci scalar along theFinslerian Ricci flow is obtained and it is proved that the Ricci flowpreserves positivity of reduced $hh$-curvature on finite time. Next, it isshown that the evolution of Ricci scalar is a parabolic-type equation and ifthe initial Finsler metric is of positive flag curvature, then the flagcurvature and the Ricci scalar remain positive as long as the solution exists.Finally, a lower bound for the Ricci scalar along the Ricci flow is obtained.

Evolution of Ricci scalar under Finsler Ricci flow