A+ CATEGORY SCIENTIFIC UNIT

Rigidity of noncompact manifolds with cyclic parallel Ricci curvature

Volume 112 / 2014

Yi Hua Deng Annales Polonici Mathematici 112 (2014), 101-108 MSC: Primary 53C21; Secondary 53C25. DOI: 10.4064/ap112-1-8

Abstract

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.

Authors

  • Yi Hua DengDepartment of Mathematics and Computational Science
    Hengyang Normal University
    421002 Hengyang, China
    e-mail

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