On Finslerian Ricci soliton

On Finslerian Ricci soliton

The notion of Ricci soliton or quasi Einstein metric is recently studied by the present authors in Finsler geometry. In compact case, it is proved that the quasi-Einstein metrics are solution to the Finslerian Ricci ow and conversely, certain form of solutions to the Finslerian Ricci ow are quasi-Einstein Finsler metrics. Here forward geodesically complete Ricci solitons are studied and some extensions, as well as, a bound for diameter of M is obtained.