由Ricci流启发的二次微分方程

Quadratic differential equations inspired by Ricci flow

利用Uhlenbeck的一个技巧,Ricci流的曲率算子满足一个用正交Lie代数定义的漂亮的演化方程.其实这个方程也可以用任何一个Lie代数来定义.这份简要的综述里讨论了相应的二次微分方程的一些性质.

After using the so-called Uhlenbeck＇s trick, the curvature operator of the Ricci flow satisfies a beautiful evolution equation defined by using the orthogonal Lie algebra. Actually this equation can be defined for all Lie algebra. In this note of a brief survey, we discuss some properties of the associated quadratic differential equations.