ON A CLASS OF FINSLER GRADIENT RICCI SOLITONS

In this paper, we study a class of Finsler measure spaces whose weighted Ricci curvature satisfies Ric infinity = cF2. This class contains all gradient Ricci solitons and Finsler Gaussian shrinking solitons. Thus Finsler measure spaces in this class are called Finsler gradient Ricci solitons. For a Randers measure space, we find sufficient and necessary conditions for this space to be a Finsler gradient Ricci soliton. In particular, we show that Randers-Finsler gradient Ricci solitons must have isotropic S-curvature. Finally, we give an equivalent condition for a Randers measure space to be a Finsler gradient Ricci soliton of constant S-curvature.

Automated summary

In this paper, the authors study a class of Finsler measure spaces whose weighted Ricci curvature satisfies Ric infinity = cF2. This class includes all gradient Ricci solitons and Finsler Gaussian shrinking solitons. Therefore, Finsler measure spaces in this class are called Finsler gradient Ricci solitons. The authors also find sufficient and necessary conditions for a Randers measure space to be a Finsler gradient Ricci soliton and prove that Randers-Finsler gradient Ricci solitons must have isotropic S-curvature. They also provide an equivalent condition for a Randers measure space to be a Finsler gradient Ricci soliton of constant S-curvature.