题  目：Flag-wise positively curved condition and homogeneous Finsler geometry

报告人：许  明，教授  (首都师范大学)

时  间：2017年10月13日 （周五）    上午10:00-11:00

地  点：五教  5106  

内容提要：

Flag curvature in Finlser geometry is a generalization of sectional curvature in Riemannian geometry, which enable us to define and study positively curved or negatively curved spaces in Finsler geometry. In this talk, we introduce a weaker version of positive curvature property which only appears in Finsler geometry, i.e. the flag-wise positively curved condition, or (FP) condition for simplicity. We show there exist abundant examples of compact coset spaces which admits non-negatively curved and flag-wise positively curved homogeneous Finsler metrics, but no positively curved homogeneous Finsler metrics. For example, S^2/times S^3 and S^6/times S^7 admits such metrics which seem "very close" to the positively curved ones. 

参考文献：

1. Homogeneous Finsler spaces and the flag-wise positively curved condition,

ar Xiv: 1604.076953

2. Examples of flag-wise positively curved spaces,

arXiv:1606.01731