学术报告

Rigidity of Einstein Four-Manifolds with Positive Sectional Curvature

阅读次数:1628

题目:Rigidity of Einstein Four-Manifolds with Positive Sectional Curvature
报告人:吴鹏 (复旦大学 上海数学中心)
地点:致远楼 103 室
时间:2018 年 06 月27 日 14:30-15:30
摘要:Einstein metrics are natural Riemannian metrics on differentiable manifolds. In dimensions 2 and 3, they must have constant sectional curvature, while in dimension 4, they are much more complicated. For the complex setting, in 1990 Tian classified Kahler-Einstein four-manifolds with positive scalar curvature, and in 2012 LeBrun classified Hermitian, Einstein four-manifolds with positive scalar curvature. For the real setting, however less is known, even assuming a (strong) condition of positive sectional curvature.
 In this talk I will first talk about some background on Einstein manifolds, then I will focus on Einstein four-manifolds with positive curvature, I will talk about my recent attempts of attacking this problem via k-positive curvature operator.

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