浙大-西湖几何分析讨论班——A class of projectively flat Finsler metrics

报告人：莫小欢教授（北京大学）

时  间：2024年10月17日（周四）16：00-17:00

地  点：海纳苑2幢106

摘  要：Projectively flat Finlser metrics on a convex domain ${U}$ in $\mathbb{R}^n$ are regular solutions to Hilbert's Fourth Problem. In this lecture, we discuss projectively flat Finlser metrics on ${U}$. We find equations that characterize these metrics with weakly orthogonal invariance, refining a theorem due to Sol$\acute{o}$rzano-Le$\acute{o}$n. As its application, we obtain infinitely many $new$ projectively flat Finlser metrics on $\mathbb{S}^{n+1}$ and determine their scalar flag curvature. These metrics contain Bryant's projective spherically symmetric Finsler metric of constant flag curvature $1$.

联系人：江文帅（wsjiang@zju.edu.cn）