报告题目: The study of affine hypersurfaces and its recent progress
报告时间: 2022-04-27 14:00——2022-04-27 16:00
报告人: 胡泽军
报告地点: 腾讯会议780-433-386
主办单位: 数据科学与人工智能学院 东北财经大学应用数学研究中心
【主讲人简介】
胡泽军,郑州大学数学与统计学院博士生导师、二级教授、中国数学会理事、国际数学期刊《Journal of Geometry》和《JP Journal of Geometry and Topology》编委。曾主持河南省杰出青年科学基金和国家自然科学基金面上项目5项。研究方向为微分几何,研究领域涉及子流形的几何与拓扑、共形微分几何、仿射微分几何,特别在等仿射超曲面和中心仿射超曲面研究中做出了一系列重要的工作。
【报告摘要】
In this talk, I will first review some of the influential results on locally strongly convex affine hypersurfaces. Then, I will introduce our works on both equiaffine and centroaffine hypersurfaces, which include the following most recent results: (1) The proof that every centroaffine Tchebychev hyperovaloid is ellipsoid; (2) The new characterizations of the ellipsoids by integral inequalities in terms of equiaffine (resp. centroaffine) invariants; (3) The classification of affine hyperspheres whose affine metric are the Riemannian product of two Riemannian metrics both having constant sectional curvatures.