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Some characterizations on critical metrics for quadratic curvature functions


Authors: Guangyue Huang and Li Chen
Journal: Proc. Amer. Math. Soc. 146 (2018), 385-395
MSC (2010): Primary 51H25; Secondary 53C21
DOI: https://doi.org/10.1090/proc/13740
Published electronically: August 1, 2017
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Abstract: Under some integral conditions, we classify closed $ n$-dimensional manifolds of which the metrics are critical for quadratic curvature functions. Moreover, under some curvature conditions, we also obtain that a critical metric must be Einstein.


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Additional Information

Guangyue Huang
Affiliation: Department of Mathematics, Henan Normal University, Xinxiang 453007, People’s Republic of China
Email: hgy@henannu.edu.cn

Li Chen
Affiliation: Faculty of Mathematics and Statistics, Hubei University, Wuhan, 430062, People’s Republic of China
Email: chernli@163.com

DOI: https://doi.org/10.1090/proc/13740
Keywords: Critical metric, quadratic functionals, Einstein
Received by editor(s): September 13, 2016
Received by editor(s) in revised form: January 5, 2017, March 1, 2017, and March 12, 2017
Published electronically: August 1, 2017
Additional Notes: The research of the authors was supported by NSFC (No. 11371018, 11671121, 11201131) and Hubei Key Laboratory of Applied Mathematics (Hubei University)
Communicated by: Guofang Wei
Article copyright: © Copyright 2017 American Mathematical Society

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