闭黎曼流形上临界度量的研究

CRITICAL POINTS FOR QUADRATIC CURVATURE FUNCTIONAL ON CLOSED MANIFOLDS

本文研究了闭黎曼流形上的双参数二次曲率泛函的临界度量,利用带Yamabe常数及曲率的pinching条件,以及我们证明了一个刚性定理。此外,我们也得到另外一些曲率条件下的刚性结果。

In this paper,the critical metrics for two-parameter quadratic curvature functionals on closed manifolds,and pinching conditions with Yamabe incariant and curvature were studied.Moreover,the results also provide a few rigidity results that involve the Weyl curvature,the trace-less Ricci curvature and the Yamabe invariant,accordingly.