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Locally conformally flat manifolds with constant scalar curvature


Authors: Huiya He and Haizhong Li
Journal: Proc. Amer. Math. Soc. 146 (2018), 5367-5378
MSC (2010): Primary 53C20, 53C21
DOI: https://doi.org/10.1090/proc/14148
Published electronically: September 17, 2018
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Abstract: Let $ (M^n,g)$ be an $ n$-dimensional $ (n\geq 4)$ compact locally conformally flat Riemannian manifold with constant scalar curvature and constant squared norm of Ricci curvature. Applying the moving frame method, we prove that such a Riemannian manifold does not exist if its Ricci curvature tensor has three distinct eigenvalues.


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Additional Information

Huiya He
Affiliation: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People’s Republic of China
Email: hhy15@mails.tsinghua.edu.cn

Haizhong Li
Affiliation: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People’s Republic of China
Email: hli@math.tsinghua.edu.cn

DOI: https://doi.org/10.1090/proc/14148
Keywords: Locally conformally flat manifold, constant scalar curvature, Ricci curvature
Received by editor(s): December 18, 2017
Published electronically: September 17, 2018
Additional Notes: The authors were supported by grant NSFC-11671224
Communicated by: Guofang Wei
Article copyright: © Copyright 2018 American Mathematical Society

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