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Guangyue Huang,Bingqing Ma,Jie Yang 대한수학회 2020 대한수학회보 Vol.57 No.6
We study rigidity results for the Einstein metrics as the critical points of a family of known quadratic curvature functionals involving the scalar curvature, the Ricci curvature and the Riemannian curvature tensor, characterized by some pointwise inequalities involving the Weyl curvature and the traceless Ricci curvature. Moreover, we also provide a few rigidity results for locally conformally flat critical metrics.
Rigidity of complete Riemannian manifolds with vanishing Bach tensor
Guangyue Huang,Bingqing Ma 대한수학회 2019 대한수학회보 Vol.56 No.5
For complete Riemannian manifolds with vanishing Bach tensor and positive constant scalar curvature, we provide a rigidity theorem characterized by some pointwise inequalities. Furthermore, we prove some rigidity results under an inequality involving $L^{\frac{n}{2}}$-norm of the Weyl curvature, the traceless Ricci curvature and the Sobolev constant.
RIGIDITY OF COMPLETE RIEMANNIAN MANIFOLDS WITH VANISHING BACH TENSOR
Huang, Guangyue,Ma, Bingqing Korean Mathematical Society 2019 대한수학회보 Vol.56 No.5
For complete Riemannian manifolds with vanishing Bach tensor and positive constant scalar curvature, we provide a rigidity theorem characterized by some pointwise inequalities. Furthermore, we prove some rigidity results under an inequality involving $L^{\frac{n}{2}}$-norm of the Weyl curvature, the traceless Ricci curvature and the Sobolev constant.