Twisted Ricci flow on a class of Finsler metrics and its solitons

In this paper, we study a geometric flow called twisted Ricci flow on a class of Finsler manifolds. We study some solitons based on the structure of the metric. The equations of the soliton are related to Killing vector fields. This forces a shrinking Ricci soliton of a Riemannian metric to be Einstein in some cases. At last, we prove the short time existence.