06-28【莫小欢】管理科研楼1418 Geometry&Topology Seminar系列讲座之067

发布者:王欣发布时间:2023-06-26浏览次数:10

告题目:A new quantity in Finsler geometry

报告人:莫小欢教授(北京大学)

时间:2023年6月28日上午10:00~11:00

地点:管理科研楼1418

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.