報(bào) 告 人：莫小歡 教授 

報(bào)告題目：On Finsler gradient Ricci solitons 

報(bào)告時(shí)間：2024年9月6日（周五）下午3：30 - 4：30 

報(bào)告地點(diǎn)：靜遠(yuǎn)樓1506學(xué)術(shù)報(bào)告廳 

主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院

報(bào)告人簡(jiǎn)介：

    莫小歡，北京大學(xué)數(shù)學(xué)科學(xué)學(xué)院教授。莫小歡教授長(zhǎng)期從事幾何學(xué)的研究工作和教學(xué)工作，主要研究興趣是黎曼-芬斯勒幾何學(xué)和幾何變分學(xué)。已發(fā)表學(xué)術(shù)論文132篇，其中被SCI收錄100余篇，論文被引用達(dá)到787次（MathSciNet）。

報(bào)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.