Speaker: Xiaohuan Mo（Peking University）
Time: 10:00-11:00, June 28, 2023
Room: Room 1418, Management and Research Building
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.
