一、报告题目：A new quantity in Finsler geometry

二、报告人：莫小欢  教授

三、时 间：2025年1月13日（星期一）15:00—16:00

四、地 点：闻理园A4-216

报告摘要：In this lecture, we discuss a new Finslerian quantity $\hat{T}$ defined by the $T$-curvature and the angular metric tensor. We show that the $\hat{T}$-curvature not only gives a measure of the failure of a Finsler metric to be of scalar flag curvature and but also has vanishing trace. We find that the $\hat{T}$-curvature is closed related the Riemann curvature, the Matsumoto torsion and the ${\Theta}$-curvature. We answer Z. Shen's an open problem in terms of the $\hat{T}$-curvature. Finally, we give a global rigidity result for Finsler metrics of negative Ricci curvature on a compact manifold via the $\hat{T}$-curvature, generalizing a theorem previously only known in the case of negatively curved Finsler metrics with scalar flag curvature.

报告人简介：莫小欢，北京大学二级教授，博士生导师。1982年浙江师范大学本科毕业，1991年浙江大学博士毕业，1995年北京大学博士后出站后留校任教。长期从事几何学的研究和教学工作。主要研究兴趣是黎曼-芬斯勒几何学和几何变分学。曾在德国、法国、美国、意大利、巴西、匈牙利等国家进行学术访问和合作研究。已发表学术论文130余篇，论文引用达到766次。

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