  The geometric flow theory and its applications turned into one of the most
intensively developing branches of modern geometry. Here, a brief introduction
to Finslerian Ricci flow and their self-similar solutions known as Ricci
solitons are given and some recent results are presented. They are a
generalization of Einstein metrics and are previously developed by the present
authors for Finsler manifolds. In the present work, it is shown that a complete
shrinking Ricci soliton Finsler manifold has a finite fundamental group.
