(1) Title: On curvatures of a class of Finsler metrics by the navigation problem
Speaker: Professor Xiaohuan Mo (莫小欢) (Peking University)
Time:  9: 30-10: 30 am, Sept. 27, 2019 (Friday)
Venue: 200-9, Sir Run Run Shaw Business Building, Yuquan Campus


Abstract: In this lecture, we discuss some basic theory of Finsler metrics. We determine the flag curvature of curvature of Finsler metric produced from {/em any} Finsler metric and {/em any} conformal field in terms of the navigation problem and therefore we provide a unifying frame work for the fundamental equations due to Bao-Robles-Shen, Cheng-Shen, Foulon and Mo-Huang. Then we study the Landsberg curvature of a Finsler metric via conformal navigation problem. We show that the Landsberg curvature of $F$ is proportional to its Cartan torsion where $F$ is the Finsler metric produced from a Landsberg metric and its closed vector field in terms of the conformal navigation problem generalizing results previously known in the cases when $F$ is a Randers metric or the Funk metric on a strongly convex domain. We also prove that the Killing navigation problem has the Landsberg curvature preserving property for a closed vector field.



(2) Title: Some fundamental problems in global Finsler geometry
Speaker: Professor Xinyue Cheng (程新跃) (Chongqing Normal University)
Time:  10: 30-11：30 am, Sept. 27, 2019 (Friday)
Venue: 200-9, Sir Run Run Shaw Business Building, Yuquan Campus

Abstract: In this talk, we introduce some important and fundamental topics in global Finsler geometry and discuss the related properties and the relationships in them. In particular, we optimize and improve the various definitions of Lie derivatives on Finsler manifolds. We also characterize the gradient vector fields  and obtain a gradient estimate for any smooth function on a Randers manifold.

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Contact person: Qiaoling Xia (xiaqiaoling@zju.edu.cn)