1-2【莫小欢】On Finsler gradient Ricci solitons

In this lecture we discuss a class of Finsler measure space whose weighted Ricci curvature satisfies Ric_{\infty}=cF^2. This class contains all gradient Ricci solitons and Finsler Gaussian 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 Finsler gradient Ricci solitons must have isotropic S-curvature. Then we explicitly construct new infinitely many n-dimensional complete Finsler gradient Ricci solitons. In particular, we find an eigenfunction and its eigenvalue for such spaces generalizing the result previously only known for the case of Gaussian shrinking soliton. Finally we give necessary and sufficient conditions on the coordinate functions for these spaces to be Euclidean measure spaces.