报告题目：A new quantity in Finsler geometry

报告时间：2024-03-15  15:00-16:00

报 告 人：莫小欢 教授 (北京大学）

报告地点：东北楼一楼报告厅

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