Abstract
In this paper, we consider some rigidity results for the Einstein metrics as the critical points of some known quadratic curvature functionals on complete manifolds, characterized by some point-wise inequalities. Moreover, we also provide rigidity results by the integral inequalities involving the Weyl curvature, the traceless Ricci curvature and the Sobolev constant, accordingly.
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Huang, G., Chen, Y. & Li, X. Rigidity of Einstein Metrics as Critical Points of Some Quadratic Curvature Functionals on Complete Manifolds. J Geom Anal 31, 7968–7988 (2021). https://doi.org/10.1007/s12220-020-00563-3
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DOI: https://doi.org/10.1007/s12220-020-00563-3