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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.

Some rigidity characterizations of Einstein metrics as critical points for quadratic curvature functionals

Guangyue Huang, Bingqing Ma, Jie Yang

Henan Normal University; Henan Normal University; Xinjiang University

Abstract

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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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