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10-13吴文俊数学重点实验室微分几何系列报告【许 明】

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

  科大主页 | 国家数学与交叉科学中心(合肥) | 中科院吴文俊数学重点实验室 |
中科院数学与系统科学研究院 | 北京国际数学研究中心 | 安徽省数学会