Homogeneous Finsler spaces with positive flag curvature, classificastion and related topics

speaker: Ming Xu (Capital Normal University, Beijing)

abstract: This talk is based on my joint works with Shaoqiang Deng, Wolfgang Ziller, Libing Huang, Zhiguang Hu and Lei Zhang. Firstly, I will briefly survey the history of the classification for homogeneous spaces of positive curvature. Secondly, I will introduce our joint works on this classification project in the context of homogeneous Finsler geometry. Thirdly, I will use a few minutes to discuss the tools we used. Finally, I will introduce a new thought for studying the positive curvature problem in Finsler geometry, defining a weaker version of positive curvature condition which only appear in Finsler geometry, the (FP) condition, i.e. for any tangent plane at any point, we can find a suitable flag pole such that the corresponding flag curvature is positive. Non-negatively curved Finsler metrics satisfying the (FP) condition seem very close to the classical positive flag curvature condition. Suprisingly, we can find many examples of compact coset spaces which admit homogeneous Finsler metrics satisfying the non-negatively curved condition and the (FP) condition, but not the positively curved condition.

timetable:
Thu 24 May, 15:40 - 16:30, Aula Dini
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