Some rigidity characterizations of Einstein metrics as critical points for quadratic curvature functionals
Bull. Korean Math. Soc.
Published online June 12, 2020
Guangyue Huang, Bingqing Ma, and Jie Yang
Henan Normal University, Xinjiang University
Abstract : We study rigidity results for the Einstein metrics as the critical points of a family of known quadratic curvature functionals involving the scalar curvature, the Ricci curvature and the Riemannian curvature tensor, characterized by some pointwise inequalities involving the Weyl curvature and the traceless Ricci curvature. Moreover, we also provide a few rigidity results for locally conformally flat critical metrics.
Keywords : Critical metric, rigidity, Einstein
MSC numbers : Primary 53C24, Secondary 53C21
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