Rigidity of noncompact manifolds with cyclic parallel Ricci curvature
Tom 112 / 2014
Annales Polonici Mathematici 112 (2014), 101-108 MSC: Primary 53C21; Secondary 53C25. DOI: 10.4064/ap112-1-8
We prove that if $M$ is a complete noncompact Riemannian manifold whose Ricci tensor is cyclic parallel and whose scalar curvature is nonpositive, then $M$ is Einstein, provided the Sobolev constant is positive and an integral inequality is satisfied.