On quasi-Einstein Finsler spaces‎

‎The notion of quasi-Einstein metric in physics is equivalent to the notion of Ricci soliton in Riemannian spaces‎. ‎Quasi-Einstein metrics serve also as solution to the Ricci flow equation‎. ‎Here‎, ‎the Riemannian metric is replaced by a Hessian matrix derived from a Finsler structure and a quasi-Einstein Finsler metric is defined‎. ‎In compact case‎, ‎it is proved that the quasi-Einstein metrics are solution < s > to the Finslerian Ricci flow and conversely‎, ‎certain form of solutions to the Finslerian Ricci flow are quasi-Einstein Finsler metrics‎.