黎曼流形上二次曲率泛函临界度量的刚性结果

Some rigidity results for critical metrics of quadratic curvature functionals on Riemannian manifolds

主要研究紧致黎曼流形上有关二次曲率泛函临界度量的刚性结果.使用有关Weyl曲率张量的不等式估计与散度定理,得到了临界度量是Einstein度量以及常截面曲率度量的分类结果.

In this paper,we study some rigidity results for Einstein metrics as the critical points of a family of known quadratic curvature functionals on compact manifolds.Using some estimates with respect to the Weyl curvature tensor and divergence theorems,we obtain that a critcal metric must be Einstein or constant sectional curvature.