汇报标题 (Title)： A new quantity in Finsler geometry
中文标题：Finsler几何中的一个新量
汇报人 (Speaker)：莫幼欢（北京大学）
汇报功夫 (Time)：2024年1月17日(周三) 16:00-17:00
汇报地址 (Place)：校本部GJ303
约请人(Inviter)：席东盟、李晋、张德凯，吴加勇
主办部门：理学院数学系
汇报提要：In this lecture, we discuss a new Finslerian quantity defined by the -curvature and the angular metric tensor. We show that the -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 -curvature is closed related the Riemann curvature, the Matsumoto torsion and the -curvature. We answer Z. Shen's an open problem in terms of the -curvature. Finally, we give a global rigidity result for Finsler metrics of negative Ricci curvature on a compact manifold via the -curvature, generalizing a theorem previously only known in the case of negatively curved Finsler metrics with scalar flag curvature.
