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Rigidity of Einstein manifolds and generalized quasi-Einstein manifolds

Volume 115 / 2015

Yi Hua Deng, Li Ping Luo, Li Jun Zhou Annales Polonici Mathematici 115 (2015), 235-240 MSC: Primary 53C25; Secondary 53C21. DOI: 10.4064/ap115-3-3

Abstract

We discuss the rigidity of Einstein manifolds and generalized quasi-Einstein manifolds. We improve a pinching condition used in a theorem on the rigidity of compact Einstein manifolds. Under an additional condition, we confirm a conjecture on the rigidity of compact Einstein manifolds. In addition, we prove that every closed generalized quasi-Einstein manifold is an Einstein manifold provided $\mu =-{1/(n-2)}$, $\lambda \leq 0$ and $\beta \leq 0$.

Authors

  • Yi Hua DengCollege of Mathematics and Statistics
    Hengyang Normal University
    Hengyang, Hunan 421002, China
    e-mail
  • Li Ping LuoCollege of Mathematics and Statistics
    Hengyang Normal University
    Hengyang, Hunan 421002, China
    e-mail
  • Li Jun ZhouCollege of Mathematics and Statistics
    Hengyang Normal University
    Hengyang, Hunan 421002, China
    e-mail

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