Locally conformally flat manifolds with constant scalar curvature

He, Huiya; Li, Haizhong

doi:10.1090/proc/14148

Locally conformally flat manifolds with constant scalar curvature
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by Huiya He and Haizhong Li

Proc. Amer. Math. Soc. 146 (2018), 5367-5378

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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