Rigidity of complete Riemannian manifolds with vanishing Bach tensor

Abstract

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.

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References in corpus (4)

• Rigidity of noncompact complete Bach-flat manifolds
• Rigidity of complete Riemannian manifolds with vanishing Bach tensor
• A sphere theorem for Bach-flat manifolds with positive constant scalar curvature
• Rigidity of Einstein metrics as critical points of some quadratic curvature functionals on complete manifolds

Cited by in corpus (2)

• Rigidity of complete Riemannian manifolds with vanishing Bach tensor
• Some rigidity characterizations of Einstein metrics as critical points for quadratic curvature functionals