报 告 人：莫小欢 教授
报告题目：On Finsler gradient Ricci solitons
报告时间：2024年9月6日（周五）下午3：30 - 4：30
报告地点：静远楼1506学术报告厅
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
莫小欢，北京大学数学科学学院教授。莫小欢教授长期从事几何学的研究工作和教学工作，主要研究兴趣是黎曼-芬斯勒几何学和几何变分学。已发表学术论文132篇，其中被SCI收录100余篇，论文被引用达到787次（MathSciNet）。
报告摘要：
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.