Rigidity of Einstein metrics as critical points of quadratic curvature functionals on closed manifolds. (October 2018) - Ma, Bingqing; Huang, Guangyue; Li, Xingxiao; Chen, Yu
Abstract: In this paper, we prove some rigidity results for the Einstein metrics as the critical points of a family of known quadratic curvature functionals on closed manifolds, characterized by some point-wise inequalities. Moreover, we also provide a few rigidity results that involve the Weyl curvature, the trace-less Ricci curvature and the Yamabe invariant, accordingly.