Bull. Korean Math. Soc. 2020; 57(6): 1367-1382
Online first article June 12, 2020 Printed November 30, 2020
https://doi.org/10.4134/BKMS.b191032
Copyright © The Korean Mathematical Society.
Guangyue Huang, Bingqing Ma, Jie Yang
Henan Normal University; Henan Normal University; Xinjiang University
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
Supported by: This work is financially supported by NSFC (Nos. 11971153, 11671121)
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