Rigidity of Einstein metrics as critical points of some quadratic curvature functionals on complete manifolds

28 Apr 2018 Huang Guangyue Chen Yu Li Xingxiao

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 trace-less Ricci curvature and the Sobolev constant, accordingly...

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  • DIFFERENTIAL GEOMETRY